CINXE.COM
Fundamental Algebraic Geometry: Grothendieck’s FGA Explained
<!DOCTYPE html> <html lang="en"> <head> <!-- cookie consent code --> <link rel="stylesheet" type="text/css" href="https://www.ams.org/css/cookieconsent.min.css" /> <script src="https://www.ams.org/js/cookieconsent.min.js"></script> <script> window.addEventListener("load", function () { window.cookieconsent.initialise({ "palette": { "popup": { "background": "#edeff5", "text": "#000000" }, "button": { "background": "#4b81e8" } }, "theme": "classic", "position": "bottom-right", "content": { "message": "This website uses cookies to ensure you get the best experience on our website.", "href": "https://www.ams.org/privacy", "dismiss": "Okay", "link": "Learn more about our privacy policy" } }) }); </script> <!-- end cookie consent code --> <!-- Google tag (gtag.js) --> <script async src="https://www.googletagmanager.com/gtag/js?id=G-26G4XFTR63"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-26G4XFTR63'); </script> <!-- Google Tag Manager --> <script> (function (w, d, s, l, i) { w[l] = w[l] || []; w[l].push({ 'gtm.start': new Date().getTime(), event: 'gtm.js' }); var f = d.getElementsByTagName(s)[0], j = d.createElement(s), dl = l != 'dataLayer' ? '&l=' + l : ''; j.async = true; j.src = 'https://www.googletagmanager.com/gtm.js?id=' + i + dl; f.parentNode.insertBefore(j, f); })(window, document, 'script', 'dataLayer', 'GTM-P3772VN');</script> <!-- End Google Tag Manager --> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1.0, minimum-scale=1" /> <title>Fundamental Algebraic Geometry: Grothendieck’s FGA Explained</title> <link rel="stylesheet" href="/lib/bootstrap/dist/css/bootstrap.min.css" /> <link rel="stylesheet" href="/css/site.css?v=la2wBcwNrtsWnRcKs9-t6qPZCC77Hs6CAduqGL_rRNM" /> <link rel="stylesheet" href="/AMS.Bookstore.Web.styles.css?v=EbYdkYcakcRZHL_Eslmh3bJ13Lr5eSLPDCBHBH67P8Q" /> <link rel="stylesheet" href="/css/modal.css?v=jRvw7By4TNDoJZ_KpsQbElRYsNpbzhWunAP5-eocRzk" /> <link rel="stylesheet" href="/css/loadingPanel.css?v=lBJGOYH_EIEBMMe17FTOETO6n2E9cwL1WhqodiMLsoM" /> <link rel="stylesheet" href="/css/cart.css?v=OO3e6LoNzay9iX1eQBG8Hnya8fMmx9ZQBbFa7WLeDZ8" /> <link rel="stylesheet" href="/css/tree.css?v=yt1z_iNvMykqt8oScR01Hf7VRyHQvVljhatJQ1CaseI" /> <script src="/lib/jquery/dist/jquery.min.js"></script> <script src="/lib/bootstrap/dist/js/bootstrap.bundle.min.js"></script> <script src="/js/site.js?v=hqP4uPRLXDoB3DGdt798csCdljKq0RvUSE-n1y2q8Dk"></script> <script src="https://kit.fontawesome.com/2ad6d7fbd6.js" crossorigin="anonymous"></script> <script src="/lib/sharethis/js/sharethis.js?v=MwmBK2LdmpagMX_OQV5w4rl5KC5hV5U2i72SiTbLwSs#property=63d912115a2f67001342bdf7&product=inline-share-buttons&source=platform"></script> <script src="/js/tree.js?v=gK9mc-ELJAYi3HDKChZgjIA89g8Xo5gXfbKPVpRVLxU"></script> <script type="text/javascript"> $(document).ready(function() { $("#ViewModelLink").addClass("active"); $(".loginLogout").click(setRedirect); $(".cartCounter").html($("#cartCountPlaceholder").html()); handleCustomShareConfig(); handleInfoHeader('2025/02/16|23:19'); }); function setRedirect() { event.preventDefault(); if ("https://bookstore.ams.org/view?ProductCode=SURV/123" == "") { // we are on the browse page, need to set propery with javascript() var returnUrl = getShareUrl(); returnUrl = encodeURIComponent(returnUrl); var baseUrl = $(this).prop("href"); var questionOrAnd = baseUrl.includes("?") ? "&" : "?"; location.href = baseUrl + questionOrAnd + "returnUrl=" + returnUrl; } else { location.href = $(this).prop("href"); } } </script> <meta property="og:url" content="https://bookstore.ams.org/SURV/123" /> <meta property="og:type" content="website" /> <meta property="og:title" content="Fundamental Algebraic Geometry: Grothendieck’s FGA Explained" /> <meta property="og:image" content="https://ebus.ams.org/ProductImages/surv-123-s-e-cov-1.jpg" /> </head> <body> <!-- Google Tag Manager (noscript) --> <noscript> <iframe b-nlceesq935 src="https://www.googletagmanager.com/ns.html?id=GTM-P3772VN" height="0" width="0" style="display:none;visibility:hidden"></iframe> </noscript> <!-- End Google Tag Manager (noscript) --> <div b-nlceesq935 id="cartCountPlaceholder" style="display:none"><div class="cart"> <a class="cart" href="https://ebus.ams.org/ebus/ShoppingCart.aspx"> <span class="showItems"> <span class="cartCountLabel"> 0 </span> </span> </a> </div></div> <div b-nlceesq935 class="headerLogoSearchContainer"> <div b-nlceesq935 role="banner" class="headerLogoSearchContainerTopRow"> <div b-nlceesq935 class="headerLogoContainer mobile"> <button b-nlceesq935 id="headerLogoMenuButton" class="headerLogoMenuContainer" onclick="openSideNav(event);" onkeypress="handleKeypressForClick(event)" tabindex="0" aria-label="Open side navigation menu"></button> <div b-nlceesq935><a b-nlceesq935 href="/" aria-label="Link to browse"><img b-nlceesq935 src="/images/ams-bookstore-logo.png" alt="AMS Logo"></a></div> <div b-nlceesq935 class="headerLogoCartContainer"> <div b-nlceesq935 id="cartCounter" class="cartCounter"> </div> </div> </div> <div b-nlceesq935 class="headerLogoContainer wide"> <a b-nlceesq935 href="/" aria-label="Link to browse"><img b-nlceesq935 src="/images/ams-bookstore-logo.png" alt="AMS Logo"></a> </div> <div b-nlceesq935 class="headerLogoRightResponsive"> <div b-nlceesq935 class="headerRightSideActionItems"> <div b-nlceesq935 class="headerNavLinks"> <ul b-nlceesq935 class="navbar-nav flex-grow-1"> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 href="https://www.ams.org" target="_blank" class="nav-link text-dark">AMS Home<span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a> </li> <li b-nlceesq935 class="nav-item"> <a class="nav-link text-dark" href="/Bookshelf">My Bookshelf</a> </li> <li b-nlceesq935 class="nav-item"> <a class="nav-link text-dark loginLogout" href="/Account/Login?returnUrl=https%3A%2F%2Fbookstore.ams.org%2Fview%3FProductCode%3DSURV%2F123">Login</a> </li> </ul> </div> <div b-nlceesq935 class="headerSearchContainer"> <link rel="stylesheet" href="/css/simpleSearch.css?v=Zp72v9BNKGS-eDr-MLHDvaAIQNNugvRUQM_CWL_F0l8" /> <link rel="stylesheet" href="//code.jquery.com/ui/1.13.1/themes/base/jquery-ui.css"> <script src="https://code.jquery.com/ui/1.13.1/jquery-ui.js"></script> <script src="/js/simpleSearch.js?v=176KrpHOwVdaFKNW5L7MgS2hJg1vembFvfNgHaMs8Vc"></script> <div role="search" id="simpleSearchContainer" class="simpleSearchContainer"> <div id="simpleSearchInputWrapper" class="simpleSearchInputWrapper" > <div class="simpleSearchMenuBtnContainer" onclick="openSideNav(event);" onkeypress="handleKeypressForClick(event)" tabindex="0"></div> <input id="simpleSearchInput" class="form-control simpleSearchInput" type="search" placeholder="Search the AMS Bookstore" autocomplete="off" aria-describedby="initInstr" aria-owns="searchSuggestionsResults" aria-expanded="false" aria-autocomplete="both" aria-activedescendant="" /><label class="hiddenLabel" for="simpleSearchInput">Search the AMS Bookstore</label> <div class="simpleSearchIconContainer"><button class="simpleSearchBtn" onclick="performSimpleSearch($('#simpleSearchInput').val())"><svg width="18" height="18" viewBox="0 0 13 13"><title>search</title><path d="m4.8495 7.8226c0.82666 0 1.5262-0.29146 2.0985-0.87438 0.57232-0.58292 0.86378-1.2877 0.87438-2.1144 0.010599-0.82666-0.28086-1.5262-0.87438-2.0985-0.59352-0.57232-1.293-0.86378-2.0985-0.87438-0.8055-0.010599-1.5103 0.28086-2.1144 0.87438-0.60414 0.59352-0.8956 1.293-0.87438 2.0985 0.021197 0.8055 0.31266 1.5103 0.87438 2.1144 0.56172 0.60414 1.2665 0.8956 2.1144 0.87438zm4.4695 0.2115 3.681 3.6819-1.259 1.284-3.6817-3.7 0.0019784-0.69479-0.090043-0.098846c-0.87973 0.76087-1.92 1.1413-3.1207 1.1413-1.3553 0-2.5025-0.46363-3.4417-1.3909s-1.4088-2.0686-1.4088-3.4239c0-1.3553 0.4696-2.4966 1.4088-3.4239 0.9392-0.92727 2.0864-1.3969 3.4417-1.4088 1.3553-0.011889 2.4906 0.45771 3.406 1.4088 0.9154 0.95107 1.379 2.0924 1.3909 3.4239 0 1.2126-0.38043 2.2588-1.1413 3.1385l0.098834 0.090049z"></path></svg></button></div> <span id="initInstr" style="display: none;">When autocomplete results are available use up and down arrows to review and enter to select. Touch device users, explore by touch or with swipe gestures.</span> <div id="simpleSearchStatus" role="status" aria-live="polite" aria-relevant="additions" class="sr-only"></div> </div> </div> <input name="__RequestVerificationToken" type="hidden" value="CfDJ8BuSt25sxbNEhWzh7kzUCWWkFye1mNdo7Qe9--c40iG_U5ljo--XE_Yh0mrUC8j3qhs8TVGJtA9bdV4ajuxnhWx3PaVxafnPDB0QQILPA6udGS_K3KB8RzAdfbDiJCCZCNDrr9yb6p6-PNf1TS-Aisg" /> <script type="text/javascript"> $(document).ready(function () { initSearchSuggestions(); }); </script> <div b-nlceesq935 class="headerNavLinks advancedSearchBtnLinkContainer"> <a id="AdvancedSearchLink" class="advancedSearchLink nav-link text-dark" href="/AdvancedSearch">Advanced Search</a> </div> <div b-nlceesq935 id="cartCounterWide" class="cartCounter wide"> </div> </div> </div> </div> </div> <div b-nlceesq935 role="navigation" class="headerNavLinks fullWidthMenu"> <ul b-nlceesq935 class="navbar-nav flex-grow-1"> <li b-nlceesq935 class="nav-item"> <a id="BrowseModelLink" class="nav-link text-dark" href="/Browse">Browse</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="belowHeaderBooksOnSaleLink" class="nav-link text-dark" href="/books-on-sale">On Sale</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="belowHeaderMAAPressLink" class="nav-link text-dark" href="/maa-press-browse">MAA Press Books</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="belowHeaderTextbookLink" class="nav-link text-dark" href="/bookstore-textbooks">Textbooks</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="belowHeaderBookSeriesLink" class="nav-link text-dark" href="/bookstore-series">Book Series</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="belowHeaderEBookCollectionsLink" class="nav-link text-dark" href="https://www.ams.org/ebooks" target="_blank">eBook Collections<span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a> </li> </ul> </div> </div> <div b-nlceesq935 role="navigation" class="sideNav"> <ul b-nlceesq935 class="sideNavUl"> <li b-nlceesq935> <button b-nlceesq935 class="headerLogoMenuContainer close" onclick="closeSideNav();" onkeypress="handleCloseSideNaveKeypress(event)" tabindex="0" aria-label="Close side navigation menu"></button> </li> <li b-nlceesq935 class="nav-item"> <a id="advancedSearchLinkSideNav" class="advancedSearchLink" class="nav-link" href="/AdvancedSearch">Advanced Search</a> </li> <li b-nlceesq935 class="nav-item"> <a id="browseModelLink" class="nav-link" href="/Browse">Browse</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="sideMenuBooksOnSaleLink" class="nav-link" href="/books-on-sale">On Sale</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="sideMenuMAAPressLink" class="nav-link" href="/maa-press-browse">MAA Press Books</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="sideMenuTextbookLink" class="nav-link" href="/bookstore-textbooks">Textbooks</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="sideMenuBookSeriesLink" class="nav-link" href="/bookstore-series">Book Series</a> </li> <li b-nlceesq935 class="nav-item"> <a b-nlceesq935 id="sideMenuEBookCollectionsLink" class="nav-link" href="https://www.ams.org/ebooks" target="_blank">eBook Collections<span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a> </li> <li b-nlceesq935 class="nav-item userAccountSection"> <a class="nav-link" href="/Bookshelf">My Bookshelf</a> </li> <li b-nlceesq935 class="nav-item"> <a class="nav-link loginLogout" href="/Account/Login?returnUrl=https%3A%2F%2Fbookstore.ams.org%2Fview%3FProductCode%3DSURV%2F123">Login</a> </li> </ul> </div> <div b-nlceesq935 class="sideNavOverlay"></div> <div b-nlceesq935 class="container"> <main b-nlceesq935 role="main" class="pb-3"> <link rel="stylesheet" href="/css/productDetail.css?v=8wTo-qBSXLRtwPS2hSRn9z0JJhfRBwjywU8YT_JBIbQ" /> <link rel="stylesheet" href="/lib/slick/dist/slick.css"> <link rel="stylesheet" href="/lib/slick/dist/slick-theme.css"> <script src="/lib/slick/dist/slick.js"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$'], ['\\(','\\)']], processEscapes: true }, loader: {load: ['[tex]/textmacros']}, tex: {packages: {'[+]': ['textmacros']}} }); </script> <script src="/js/view.js?v=_C42r0h9hUiY7WdI7n_pmeH7hE79qf9vcFdDdchBPJk"></script> <script type="text/javascript"> productDetailObj = {"ProductId":12772,"ProductCode":"SURV/123","Title":"Fundamental Algebraic Geometry","Subtitle":"Grothendieck\u0026rsquo;s FGA Explained","AMSFlags":"RBS","MSCs":"14-01||P,14C20||P,13D10||P,14D15||P,14K30||P,18F10||P,18D30||P","CopyrightYear":"2005","PageCount":"339","CoverType":"H","SeriesCode":"SURV","Series":"Mathematical Surveys and Monographs","Subseries":"","ProductClassCode":"BS","Volume":"123","ProductDescription":"\u003Cp\u003E Alexander Grothendieck\u0027s concepts turned out to be astoundingly powerful and productive, truly revolutionizing algebraic geometry. He sketched his new theories in talks given at the S\u0026eacute;minaire Bourbaki between 1957 and 1962. He then collected these lectures in a series of articles in \u003Cspan style=\u0022font-style:italic\u0022\u003EFondements de la g\u0026eacute;om\u0026eacute;trie alg\u0026eacute;brique\u003C/span\u003E (commonly known as FGA). \u003Cbr /\u003E\u003Cbr /\u003E Much of FGA is now common knowledge. However, some of it is less well known, and only a few geometers are familiar with its full scope. The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), is to fill in the gaps in Grothendieck\u0027s very condensed outline of his theories. The four main themes discussed in the book are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The authors present complete proofs of the main results, using newer ideas to promote understanding whenever necessary, and drawing connections to later developments. \u003Cbr /\u003E\u003Cbr /\u003E With the main prerequisite being a thorough acquaintance with basic scheme theory, this book is a valuable resource for anyone working in algebraic geometry.\u003C/p\u003E ","Readership":"\u003Cp\u003EGraduate students and research mathematicians interested in\nalgebraic geometry.\u003C/p\u003E","SmallImage":"https://ebus.ams.org/ProductImages/surv-123-s-e-cov-1.jpg","LargeImage":"https://ebus.ams.org/ProductImages/surv-123-s-e-cov-1.jpg","Alt1SmallImage":"surv-123-s-e-back-1.jpg","Alt1LargeImage":"surv-123-s-e-back-1.jpg","Alt2SmallImage":"","Alt2LargeImage":"","DefaultImageAltText":"Fundamental Algebraic Geometry","Alt1ImageAltText":"Back Cover for Fundamental Algebraic Geometry","Alt2ImageAltText":"Fundamental Algebraic Geometry","Imprint":"","PublisherText":"","CooperationText":"","OutOfStockReason":"ASO","NextReceiptDate":"1900-01-01T00:00:00","AdditionalAuthorText":"","Distribution":"","SeriesDistribution":"","AdditionalSeriesText":"","RelatedCustomers":[{"RelationshipType":"AUTHOR","FullName":"Barbara Fantechi","FirstName":null,"MiddleName":null,"LastName":null,"Suffix":null,"MasterCustomerId":null,"MRAuthorId":null,"Email":null,"CustomerSequence":1,"Affiliation":"SISSA, Trieste, Italy","AffiliationSequence":1,"FirstEditor":false,"Url":null,"Description":null,"BookReviewId":0},{"RelationshipType":"AUTHOR","FullName":"Lothar G\u0026ouml;ttsche","FirstName":null,"MiddleName":null,"LastName":null,"Suffix":null,"MasterCustomerId":null,"MRAuthorId":null,"Email":null,"CustomerSequence":2,"Affiliation":"International Centre for Theoretical Physics, Trieste, Italy","AffiliationSequence":1,"FirstEditor":false,"Url":null,"Description":null,"BookReviewId":0},{"RelationshipType":"AUTHOR","FullName":"Luc Illusie","FirstName":null,"MiddleName":null,"LastName":null,"Suffix":null,"MasterCustomerId":null,"MRAuthorId":null,"Email":null,"CustomerSequence":3,"Affiliation":"Universit\u0026eacute; Paris\u0026ndash;Sud, Orsay, France","AffiliationSequence":1,"FirstEditor":false,"Url":null,"Description":null,"BookReviewId":0},{"RelationshipType":"AUTHOR","FullName":"Steven L. Kleiman","FirstName":null,"MiddleName":null,"LastName":null,"Suffix":null,"MasterCustomerId":null,"MRAuthorId":null,"Email":null,"CustomerSequence":4,"Affiliation":"MIT, Cambridge, MA","AffiliationSequence":1,"FirstEditor":false,"Url":null,"Description":null,"BookReviewId":0},{"RelationshipType":"AUTHOR","FullName":"Nitin Nitsure","FirstName":null,"MiddleName":null,"LastName":null,"Suffix":null,"MasterCustomerId":null,"MRAuthorId":null,"Email":null,"CustomerSequence":5,"Affiliation":"Tata Institute of Fundamental Research, Mumbai, India","AffiliationSequence":1,"FirstEditor":false,"Url":null,"Description":null,"BookReviewId":0},{"RelationshipType":"AUTHOR","FullName":"Angelo Vistoli","FirstName":null,"MiddleName":null,"LastName":null,"Suffix":null,"MasterCustomerId":null,"MRAuthorId":null,"Email":null,"CustomerSequence":6,"Affiliation":"Universit\u0026agrave; di Bologna, Bologna, Italy","AffiliationSequence":1,"FirstEditor":false,"Url":null,"Description":null,"BookReviewId":0}],"AddToCartItems":[{"ProductId":12773,"ProductCode":"SURV/123.S","ISBN":"978-0-8218-4245-4","RelatedType":"SOFTCOVER","PageCount":"339","CoverType":"S","OutOfStockReason":"","NextReceiptDate":"0001-01-01T00:00:00","RateItems":[{"RateStructure":"LIST","RateCode":"STD","Price":129.00},{"RateStructure":"MAA","RateCode":"STD","Price":116.10},{"RateStructure":"MEM","RateCode":"STD","Price":103.20}]},{"ProductId":18794957,"ProductCode":"SURV/123.S.E","ISBN":"978-1-4704-1350-7","RelatedType":"ELECTRONIC","PageCount":"339","CoverType":"E","OutOfStockReason":"","NextReceiptDate":"0001-01-01T00:00:00","RateItems":[{"RateStructure":"LIST","RateCode":"STD","Price":125.00},{"RateStructure":"MAA","RateCode":"STD","Price":112.50},{"RateStructure":"MEM","RateCode":"STD","Price":100.00}]},{"ProductId":1314336555,"ProductCode":"SURV/123.S.B","ISBN":null,"RelatedType":"BUNDLE","PageCount":"339","CoverType":"S","OutOfStockReason":"","NextReceiptDate":"0001-01-01T00:00:00","RateItems":[{"RateStructure":"LIST","RateCode":"STD","Price":191.50},{"RateStructure":"MAA","RateCode":"STD","Price":172.35},{"RateStructure":"MEM","RateCode":"STD","Price":153.20}]}],"TOCItems":[{"Title":"Chapters","Contributors":null,"SeqNo":1,"StartPage":0,"EndPage":0,"Level":0,"MrArticleId":null,"FileUrl":null},{"Title":"1. Preliminary notions","Contributors":null,"SeqNo":2,"StartPage":7,"EndPage":12,"Level":1,"MrArticleId":"","FileUrl":null},{"Title":"2. Contravariant functors","Contributors":null,"SeqNo":3,"StartPage":13,"EndPage":40,"Level":1,"MrArticleId":"","FileUrl":null},{"Title":"3. Fibered categories","Contributors":null,"SeqNo":4,"StartPage":41,"EndPage":66,"Level":1,"MrArticleId":"","FileUrl":null},{"Title":"4. Stacks","Contributors":null,"SeqNo":5,"StartPage":67,"EndPage":104,"Level":1,"MrArticleId":"","FileUrl":null},{"Title":"5. Construction of Hilbert and Quot schemes","Contributors":null,"SeqNo":6,"StartPage":107,"EndPage":137,"Level":1,"MrArticleId":"","FileUrl":null},{"Title":"6. Elementary deformation theory","Contributors":null,"SeqNo":7,"StartPage":143,"EndPage":158,"Level":1,"MrArticleId":"","FileUrl":null},{"Title":"7. Hilbert schemes of points","Contributors":null,"SeqNo":8,"StartPage":159,"EndPage":178,"Level":1,"MrArticleId":"","FileUrl":null},{"Title":"8. Grothendieck\u0026rsquo;s existence theorem in formal geometry","Contributors":null,"SeqNo":9,"StartPage":181,"EndPage":233,"Level":1,"MrArticleId":"","FileUrl":null},{"Title":"9. The Picard scheme","Contributors":null,"SeqNo":10,"StartPage":237,"EndPage":301,"Level":1,"MrArticleId":"","FileUrl":null}],"ReviewItems":[{"ReviewText":"\u003Cp\u003EAll together, this\nbook\nmust be seen as a highly valuable addition to Grotherndieck\u0027s fundamental\nclassic FGA, and as a superb contribution to the propagation of his pioneering\nwork just as well. It is fair to say that, for the first time, the wealth of\nGrotherndieck\u0027s FGA has been made accessible to the entire community of\nalgebraic geometers, including non-specialist, young researchers, and seasoned\ngraduate students. The authors have endeavoured to elaborate Grothendieck\u0027s\ningenious, epoch-making outlines in the greatest possible clarity and\ndetailedness, with complete proofs given throughout...ought to be in the\nlibrary of anyone using modern algebraic geometry in his (or her) research.\u003C/p\u003E\n","Source":"\u003Cspan style=\u0022font-style:italic\u0022\u003EZentralblatt MATH\u003C/span\u003E","SeqNo":1}],"AwardItems":[],"RevisionItems":[],"FileItems":[{"FileTypeCode":"SUP","FileName":"surv-123","SortOrder":7,"DisplayName":"","FullUrl":"https://www.ams.org/publications/authors/books/postpub/surv-123","RelativeUrl":null}],"CrossSellProducts":[],"SetProducts":[],"IncludedInSets":[],"AllowCopyrightPermissionFlag":"true","EpubISBN":"","GetPermissionsItems":[{"ProductId":12772,"ProductCode":null,"ISBN":"978-0-8218-3541-8","RelatedType":"ORIGINAL","CoverType":"H"},{"ProductId":12773,"ProductCode":null,"ISBN":"978-0-8218-4245-4","RelatedType":"SOFTCOVER","CoverType":"S"}],"ProductOptions":[],"PointsEligibleFlag":"Y","ProductMedia":[{"LargeImage":"https://ebus.ams.org/ProductImages/surv-123-s-e-cov-1.jpg","SmallImage":"https://ebus.ams.org/ProductImages/surv-123-s-e-cov-1.jpg","MediaFileType":"IMAGE","AltText":"Fundamental Algebraic Geometry","FullUrl":"","Sort":1,"YoutubeId":""},{"LargeImage":"https://ebus.ams.org/ProductImages/surv-123-s-e-back-1.jpg","SmallImage":"https://ebus.ams.org/ProductImages/surv-123-s-e-back-1.jpg","MediaFileType":"IMAGE","AltText":null,"FullUrl":"","Sort":2,"YoutubeId":""}],"InstructorsManualFlag":"N","InstructorsSolutionManualFlag":"N","ProductText":[{"TextTypeCode":"READERSHIP","Text":"\u003Cp\u003EGraduate students and research mathematicians interested in\r\nalgebraic geometry.\u003C/p\u003E","TextHtml":"\u003Cp\u003EGraduate students and research mathematicians interested in algebraic geometry.\u003C/p\u003E","SourceHtml":"","SeqNo":0},{"TextTypeCode":"REVIEW","Text":"\u003Cp\u003EAll together, this\r\nbook\r\nmust be seen as a highly valuable addition to Grotherndieck\u0027s fundamental\r\nclassic FGA, and as a superb contribution to the propagation of his pioneering\r\nwork just as well. It is fair to say that, for the first time, the wealth of\r\nGrotherndieck\u0027s FGA has been made accessible to the entire community of\r\nalgebraic geometers, including non-specialist, young researchers, and seasoned\r\ngraduate students. The authors have endeavoured to elaborate Grothendieck\u0027s\r\ningenious, epoch-making outlines in the greatest possible clarity and\r\ndetailedness, with complete proofs given throughout...ought to be in the\r\nlibrary of anyone using modern algebraic geometry in his (or her) research.\u003C/p\u003E","TextHtml":"\u003Cp\u003EAll together, this book must be seen as a highly valuable addition to Grotherndieck\u0027s fundamental classic FGA, and as a superb contribution to the propagation of his pioneering work just as well. It is fair to say that, for the first time, the wealth of Grotherndieck\u0027s FGA has been made accessible to the entire community of algebraic geometers, including non-specialist, young researchers, and seasoned graduate students. The authors have endeavoured to elaborate Grothendieck\u0027s ingenious, epoch-making outlines in the greatest possible clarity and detailedness, with complete proofs given throughout...ought to be in the library of anyone using modern algebraic geometry in his (or her) research.\u003C/p\u003E","SourceHtml":"\u003Ci\u003EZentralblatt MATH\u003C/i\u003E","SeqNo":1},{"TextTypeCode":"REVIEW_CAT","Text":"\u003Cp\u003EIt is\r\nfair to\r\nsay that, for the first time, the wealth of\r\nGrotherndieck\u0027s FGA has been made accessible to the entire community of\r\nalgebraic geometers, including non-specialist, young researchers, and seasoned\r\ngraduate students....ought to be in the\r\nlibrary of anyone using modern algebraic geometry in his (or her) research.\r\n\u003C/p\u003E","TextHtml":"\u003Cp\u003EIt is fair to say that, for the first time, the wealth of Grotherndieck\u0027s FGA has been made accessible to the entire community of algebraic geometers, including non-specialist, young researchers, and seasoned graduate students....ought to be in the library of anyone using modern algebraic geometry in his (or her) research. \u003C/p\u003E","SourceHtml":"\u003Ci\u003EZentralblatt MATH\u003C/i\u003E","SeqNo":2},{"TextTypeCode":"TEXT","Text":"\u003Cp\u003EAlexander Grothendieck\u0027s concepts turned out to be\r\nastoundingly powerful and productive, truly revolutionizing algebraic\r\ngeometry. He sketched his new theories in talks given at the\r\nS\u0026eacute;minaire Bourbaki between 1957 and 1962. He then collected\r\nthese lectures in a series of articles in \u003Cem\u003EFondements de la\r\ng\u0026eacute;om\u0026eacute;trie alg\u0026eacute;brique\u003C/em\u003E (commonly known as\r\nFGA).\u003C/p\u003E\r\n\u003Cp\u003EMuch of FGA is now common knowledge. However, some of it is less\r\nwell known, and only a few geometers are familiar with its full\r\nscope. The goal of the current book, which resulted from the 2003\r\nAdvanced School in Basic Algebraic Geometry (Trieste, Italy), is to\r\nfill in the gaps in Grothendieck\u0027s very condensed outline of his\r\ntheories. The four main themes discussed in the book are descent\r\ntheory, Hilbert and Quot schemes, the formal existence theorem, and\r\nthe Picard scheme. The authors present complete proofs of the main\r\nresults, using newer ideas to promote understanding whenever\r\nnecessary, and drawing connections to later developments.\r\n\u003C/p\u003E\r\n\u003Cp\u003EWith the main prerequisite being a thorough acquaintance with basic\r\nscheme theory, this book is a valuable resource for anyone working in\r\nalgebraic geometry.\u003C/p\u003E","TextHtml":"\u003Cp\u003EAlexander Grothendieck\u0027s concepts turned out to be astoundingly powerful and productive, truly revolutionizing algebraic geometry. He sketched his new theories in talks given at the S\u0026eacute;minaire Bourbaki between 1957 and 1962. He then collected these lectures in a series of articles in \u003Cem\u003EFondements de la g\u0026eacute;om\u0026eacute;trie alg\u0026eacute;brique\u003C/em\u003E (commonly known as FGA).\u003C/p\u003E\u003Cp\u003EMuch of FGA is now common knowledge. However, some of it is less well known, and only a few geometers are familiar with its full scope. The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), is to fill in the gaps in Grothendieck\u0027s very condensed outline of his theories. The four main themes discussed in the book are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The authors present complete proofs of the main results, using newer ideas to promote understanding whenever necessary, and drawing connections to later developments. \u003C/p\u003E\u003Cp\u003EWith the main prerequisite being a thorough acquaintance with basic scheme theory, this book is a valuable resource for anyone working in algebraic geometry.\u003C/p\u003E","SourceHtml":"","SeqNo":0},{"TextTypeCode":"TEXT_COVER4","Text":"\u003Cp\u003EAlexander Grothendieck introduced many concepts into\r\nalgebraic geometry; they turned out to be astoundingly powerful and productive\r\nand truly revolutionized the subject. Grothendieck sketched his new theories\r\nin a series of talks at the S\u0026eacute;minaire Bourbaki between 1957 and 1962 and\r\ncollected his write-ups in a volume entitled \u0026ldquo;Fondements de la\r\nG\u0026eacute;om\u0026eacute;trie Alg\u0026eacute;brique,\u0026rdquo; known as FGA.\u003C/p\u003E\r\n\u003Cp\u003EMuch of FGA is now common knowledge; however, some of FGA is less well\r\nknown, and its full scope is familiar to few. The present\r\nbook resulted from the 2003 \u0026ldquo;Advanced School in Basic Algebraic\r\nGeometry\u0026rdquo; at the ICTP in Trieste, Italy. The book aims to fill in\r\nGrothendieck\u0027s brief sketches. There are four themes: descent theory,\r\nHilbert and Quot schemes, the formal existence theorem, and the Picard\r\nscheme. Most results are proved in full detail; furthermore, newer\r\nideas are introduced to promote understanding, and many connections are\r\ndrawn to newer developments.\u003C/p\u003E\r\n\u003Cp\u003EThe main prerequisite is a thorough acquaintance with basic scheme\r\ntheory. Thus this book is a valuable resource for anyone doing\r\nalgebraic geometry.\u003C/p\u003E","TextHtml":"\u003Cp\u003EAlexander Grothendieck introduced many concepts into algebraic geometry; they turned out to be astoundingly powerful and productive and truly revolutionized the subject. Grothendieck sketched his new theories in a series of talks at the S\u0026eacute;minaire Bourbaki between 1957 and 1962 and collected his write-ups in a volume entitled \u0026ldquo;Fondements de la G\u0026eacute;om\u0026eacute;trie Alg\u0026eacute;brique,\u0026rdquo; known as FGA.\u003C/p\u003E\u003Cp\u003EMuch of FGA is now common knowledge; however, some of FGA is less well known, and its full scope is familiar to few. The present book resulted from the 2003 \u0026ldquo;Advanced School in Basic Algebraic Geometry\u0026rdquo; at the ICTP in Trieste, Italy. The book aims to fill in Grothendieck\u0027s brief sketches. There are four themes: descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. Most results are proved in full detail; furthermore, newer ideas are introduced to promote understanding, and many connections are drawn to newer developments.\u003C/p\u003E\u003Cp\u003EThe main prerequisite is a thorough acquaintance with basic scheme theory. Thus this book is a valuable resource for anyone doing algebraic geometry.\u003C/p\u003E","SourceHtml":"","SeqNo":0},{"TextTypeCode":"TEXT_FEATURE","Text":"\u003Cp\u003EAlexander Grothendieck\u0027s work introduced powerful\r\nconcepts to algebraic geometry, truly revolutionizing the discipline. His\r\ntheory of descent remains one of the main tools in modern algebraic geometry,\r\nbut for some time there had been no detailed exposition of this theory. This\r\nbook offers an exposition of Grothendieck\u0027s results while also presenting\r\nnewer ideas.\u003C/p\u003E\r\n\u003Cp\u003EThe book, based on notes handed out at the Advanced School in Basic\r\nAlgebraic Geometry at the International Centre for Theoretical Physics in 2003,\r\nbuilds on the results of Grothendieck\u0027s volume \u0022Fondements de la\r\nG\u0026eacute;om\u0026eacute;trie Alg\u0026eacute;brique.\u0022 The text\u0027s four main themes are\r\ndescent theory, Hilbert and Quot schemes, the formal existence theorem, and the\r\nPicard scheme. The chapter that addresses the Picard scheme offers a\r\nfascinating and extensive discussion of the development of the ideas that led\r\nto it.\u003C/p\u003E\r\n\u003Cp\u003EThe text fills in Grothendieck\u0027s outline and introduces newer ideas to\r\npromote understanding. The text draws connections to subsequent developments;\r\nfor example, descent theory is written in the language of Grothendieck\r\ntopologies, which Grothendieck introduced later.\u003C/p\u003E\r\n\u003Cp\u003EThis book constitutes a valuable resource for anyone working in algebraic\r\ngeometry, with a thorough acquaintance with basic scheme theory as the main\r\nprerequisite. It is an important work for reviewing the progress of\r\nGrothendieck\u0027s concepts and serving as a source of references for future work.\r\n\u003C/p\u003E","TextHtml":"\u003Cp\u003EAlexander Grothendieck\u0027s work introduced powerful concepts to algebraic geometry, truly revolutionizing the discipline. His theory of descent remains one of the main tools in modern algebraic geometry, but for some time there had been no detailed exposition of this theory. This book offers an exposition of Grothendieck\u0027s results while also presenting newer ideas.\u003C/p\u003E\u003Cp\u003EThe book, based on notes handed out at the Advanced School in Basic Algebraic Geometry at the International Centre for Theoretical Physics in 2003, builds on the results of Grothendieck\u0027s volume \u0022Fondements de la G\u0026eacute;om\u0026eacute;trie Alg\u0026eacute;brique.\u0022 The text\u0027s four main themes are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The chapter that addresses the Picard scheme offers a fascinating and extensive discussion of the development of the ideas that led to it.\u003C/p\u003E\u003Cp\u003EThe text fills in Grothendieck\u0027s outline and introduces newer ideas to promote understanding. The text draws connections to subsequent developments; for example, descent theory is written in the language of Grothendieck topologies, which Grothendieck introduced later.\u003C/p\u003E\u003Cp\u003EThis book constitutes a valuable resource for anyone working in algebraic geometry, with a thorough acquaintance with basic scheme theory as the main prerequisite. It is an important work for reviewing the progress of Grothendieck\u0027s concepts and serving as a source of references for future work. \u003C/p\u003E","SourceHtml":"","SeqNo":0},{"TextTypeCode":"TEXT_BLURB","Text":"\u003Cp\u003EThis book offers a detailed exposition of Alexander\r\nGrothendieck\u0027s theory of descent, with further ideas not presented in previous\r\nworks. Areas addressed include Hilbert and Quot schemes, the formal existence\r\ntheorem, and the Picard scheme. The book fills in the outline presented in\r\nGrothendieck\u0027s \u0022Fondements de la G\u0026eacute;om\u0026eacute;trie Alg\u0026eacute;brique,\u0022\r\nand draws connections to subsequent developments.\u003C/p\u003E","TextHtml":"\u003Cp\u003EThis book offers a detailed exposition of Alexander Grothendieck\u0027s theory of descent, with further ideas not presented in previous works. Areas addressed include Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The book fills in the outline presented in Grothendieck\u0027s \u0022Fondements de la G\u0026eacute;om\u0026eacute;trie Alg\u0026eacute;brique,\u0022 and draws connections to subsequent developments.\u003C/p\u003E","SourceHtml":"","SeqNo":0},{"TextTypeCode":"TEXT_SUMMARY","Text":"\u003Cp\u003EA detailed exposition of Grothendieck\u0027s results that\r\nrevolutionized algebraic geometry, including some of his lesser-known theories\r\n\u003C/p\u003E","TextHtml":"\u003Cp\u003EA detailed exposition of Grothendieck\u0027s results that revolutionized algebraic geometry, including some of his lesser-known theories \u003C/p\u003E","SourceHtml":"","SeqNo":0}],"AllowDeskExamCopyRequest":"N","EstimatedPagesFlag":"N","AddToCartFlag":"N","DisplayAuthorEditorFlag":"B"}; isbnArray.push({ ProductId: "12772", RelatedType: "ORIGINAL", ISBN: "978-0-8218-3541-8", CoverType: "H" }); isbnArray.push({ ProductId: "12773", RelatedType: "SOFTCOVER", ISBN: "978-0-8218-4245-4", CoverType: "S" }); </script> <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <input type="hidden" id="hdnProductCode" name="PersonId" value="SURV/123" /> <div id="loadingPanel" class="productDetailLoadingPanel containedToParent"> <div> <div class="sp sp-3balls"></div> </div> </div> <div id="productDetailAddedToCart" class="productDetailAddedToCartContainer jmodal"> <div id="productDetailAddedToCartLoading" class="productDetailLoadingPanel hideContents"> <div> <div class="sp sp-3balls"></div> </div> </div> <div class="productDetailAddedToCartContainer"> <div class="modalHeaderContainer"> <div class="modalIcon"> </div> </div> <div class="productDetailAddedToCartMessage success"> Item Successfully Added to Cart </div> <div class="productDetailAddedToCartMessage error"> An error was encountered while trying to add the item to the cart. Please try again. </div> <div class="productDetailAddedToCartBtnContainer success"> <div> <a id="productDetailAddedToCartContinueBtn" href="#" rel="jmodal:close" class="productDetailAddedToCartContinueBtn">Continue Shopping</a> </div> <div> <a id="productDetailAddedToCartCheckoutBtn" href="https://ebus.ams.org/ebus/ShoppingCart.aspx" target="_self" class="productDetailAddedToCartCheckoutBtn">Go to Checkout</a> </div> </div> <div class="productDetailAddedToCartBtnContainer error"> <div> <a id="productDetailAddedToCartErrorOKBtn" href="#" rel="jmodal:close" class="productDetailAddedToCartErrorOKBtn">OK</a> </div> </div> </div> </div> <div id="productDetailSelectAllOptions" class="jmodal"> <div class="productDetailSelectAllOptionsContainer"> <div class="productDetailSelectAllOptionsMessage warning"> Please make all selections above before adding to cart </div> <div class="productDetailSelectAllOptionsMessageBtnContainer"> <div> <a id="productDetailSelectAllOptionsOkBtn" href="#" rel="jmodal:close" class="productDetailOkBtn">OK</a> </div> </div> </div> </div> <div class="productDetailContainer"> <div class="productDetailTopPane"> <div id="productDetailShareWrapper" class="jmodal productDetailShareModal"> <div class="productDetailShareContainer"> <div id="sharethis-button-container"></div> <div class="productDetailShareInfo"> Share this page via the icons above, or by copying the link below: </div> <div id="productDetailShareLinkInputContainer" class="productDetailShareLinkInputContainer"> <div id="productDetailShareLinkDisplay" class="productDetailShareLinkDisplay"></div> </div> <div class="productDetailShareCopyToClipboardBtnContainer"> <div class="productDetailShareCopyToClipboardBtn" onclick="copyShareToClipboard();" onkeypress="handleKeypressForClick(event)" tabindex="0"> Copy To Clipboard </div> <div class="productDetailShareCopyToClipboardSuccess"> <div class="productDetailShareCopyToClipboardSuccessMessage">Successfully Copied!</div> </div> </div> </div> </div> <div class="productDetailShareLinkContainer" onclick="javascript:showShareModal();" onkeypress="handleKeypressForClick(event)" tabindex="0"> <div class="productDetailShareLinkBtn"></div> </div> <!-- One Column --> <div class="productDetailOneColumn"> <div class="productDetailProductDescription"> <div class="productDetailTitle"> <span id="lblProductTitle">Fundamental Algebraic Geometry: Grothendieck’s FGA Explained</span> <div class="productDetailTitleShareSpacer"> </div> </div> <div class="productDetailAuthorContainer"> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_0" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Barbara Fantechi')">Barbara Fantechi</a></span> <input id="lblAuthorEditorFullnameHtml_0" type="hidden" value="Barbara Fantechi"/> <span id="lblAuthorEditSpacer_0" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_0" class="productDetailProductDescriptionAuthorAffiliation">SISSA, Trieste, Italy</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_1" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Lothar G&ouml;ttsche')">Lothar Göttsche</a></span> <input id="lblAuthorEditorFullnameHtml_1" type="hidden" value="Lothar G&ouml;ttsche"/> <span id="lblAuthorEditSpacer_1" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_1" class="productDetailProductDescriptionAuthorAffiliation">International Centre for Theoretical Physics, Trieste, Italy</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_2" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Luc Illusie')">Luc Illusie</a></span> <input id="lblAuthorEditorFullnameHtml_2" type="hidden" value="Luc Illusie"/> <span id="lblAuthorEditSpacer_2" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_2" class="productDetailProductDescriptionAuthorAffiliation">Université Paris–Sud, Orsay, France</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_3" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Steven L. Kleiman')">Steven L. Kleiman</a></span> <input id="lblAuthorEditorFullnameHtml_3" type="hidden" value="Steven L. Kleiman"/> <span id="lblAuthorEditSpacer_3" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_3" class="productDetailProductDescriptionAuthorAffiliation">MIT, Cambridge, MA</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_4" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Nitin Nitsure')">Nitin Nitsure</a></span> <input id="lblAuthorEditorFullnameHtml_4" type="hidden" value="Nitin Nitsure"/> <span id="lblAuthorEditSpacer_4" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_4" class="productDetailProductDescriptionAuthorAffiliation">Tata Institute of Fundamental Research, Mumbai, India</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_5" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Angelo Vistoli')">Angelo Vistoli</a></span> <input id="lblAuthorEditorFullnameHtml_5" type="hidden" value="Angelo Vistoli"/> <span id="lblAuthorEditSpacer_5" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_5" class="productDetailProductDescriptionAuthorAffiliation">Università di Bologna, Bologna, Italy</span> </div> </div> <div class="productDetailImageContainer"> <img id="productDetailImage" class="productDetailLargeImage" onerror="replaceImageError(this);" src="https://ebus.ams.org/ProductImages/surv-123-s-e-cov-1.jpg" title="" style="" alt="Fundamental Algebraic Geometry"> </div> <div id="productDetailOneColumnAltImages"> </div> <div class="productDetailFlagIconContainer"> </div> <div> <div class="productDetailTypeContainer "> <div class="productDetailType"> <div class="productDetailBookTypeChoose"> <button ID="btnBookType_0" class="productDetailBookTypeButton active " data-book-type="SOFTCOVER" onclick="selectBookType('SOFTCOVER');">Softcover</button> <button ID="btnBookType_1" class="productDetailBookTypeButton " data-book-type="ELECTRONIC" onclick="selectBookType('ELECTRONIC');">eBook</button> <button ID="btnBookType_2" class="productDetailBookTypeButton bundleItem" data-book-type="BUNDLE_S" onclick="selectBookType('BUNDLE_S');">Softcover + eBook<br><span class='productDetailBundleItemButtonSubtext'>Save 50% on eBook!</span></button> </div> </div> </div> <div class="productDetailCartItemContainer"> <div id="productDetailDIV_0" class="productDetailAddToCartContainer active " data-book-type="SOFTCOVER" data-product-id="12773"> <table width="100%"> <tbody> <tr class="productDetailAddToCartRow"> <td> <span id="lblISBNType_0" class="productDetailAddToCart">Softcover </span><span class="productDetailAddToCart">ISBN: </span> </td> <td> <span id="lblISBN_0" class="productDetailAddToCartValue">978-0-8218-4245-4</span> </td> </tr> <tr class="productDetailAddToCartRow"> <td> <span class="productDetailAddToCart">Product Code: </span> </td> <td> <span id="lblProductCode_0" class="productDetailAddToCartValue">SURV/123.S</span> </td> </tr> </tbody> </table> <div class="productDetailAddToCartRow productDetailAddToCartRateContainer"> <table width="100%"> <tbody> <tr id="productDetailAddToCartRateDIV_0" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">List Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$129.00</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_1" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">MAA Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$116.10</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_2" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">AMS Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$103.20</span> </td> </tr> </tbody> </table> </div> </div> <div id="productDetailDIV_1" class="productDetailAddToCartContainer " data-book-type="ELECTRONIC" data-product-id="18794957"> <table width="100%"> <tbody> <tr class="productDetailAddToCartRow"> <td> <span id="lblISBNType_1" class="productDetailAddToCart">eBook </span><span class="productDetailAddToCart">ISBN: </span> </td> <td> <span id="lblISBN_1" class="productDetailAddToCartValue">978-1-4704-1350-7</span> </td> </tr> <tr class="productDetailAddToCartRow"> <td> <span class="productDetailAddToCart">Product Code: </span> </td> <td> <span id="lblProductCode_1" class="productDetailAddToCartValue">SURV/123.S.E</span> </td> </tr> </tbody> </table> <div class="productDetailAddToCartRow productDetailAddToCartRateContainer"> <table width="100%"> <tbody> <tr id="productDetailAddToCartRateDIV_0" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">List Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$125.00</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_1" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">MAA Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$112.50</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_2" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">AMS Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$100.00</span> </td> </tr> </tbody> </table> </div> </div> <div id="productDetailDIV_2" class="productDetailAddToCartContainer " data-book-type="BUNDLE_S" data-product-id="1314336555"> <table width="100%"> <tbody> <tr class="productDetailAddToCartRow"> <td> <span id="lblISBNType_bundle_print_2" class="productDetailAddToCart">Softcover </span><span class="productDetailAddToCart">ISBN: </span> </td> <td> <span id="lblISBN_bundle_print_2" class="productDetailAddToCartValue">978-0-8218-4245-4</span> </td> </tr> <tr class="productDetailAddToCartRow"> <td> <span id="lblISBNType_bundle_electronic_2" class="productDetailAddToCart">eBook: </span><span class="productDetailAddToCart">ISBN: </span> </td> <td> <span id="lblISBN_bundle_electronic_2" class="productDetailAddToCartValue">978-1-4704-1350-7</span> </td> </tr> <tr class="productDetailAddToCartRow"> <td> <span class="productDetailAddToCart">Product Code: </span> </td> <td> <span id="lblProductCode_2" class="productDetailAddToCartValue">SURV/123.S.B</span> </td> </tr> </tbody> </table> <div class="productDetailAddToCartRow productDetailAddToCartRateContainer"> <table width="100%"> <tbody> <tr id="productDetailAddToCartRateDIV_0" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">List Price:</span> </td> <td> <span class="productDetailAddToCartRateValue strike">$254.00</span> <span class="productDetailAddToCartRateValue ">$191.50</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_1" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">MAA Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue strike">$228.60</span> <span class="productDetailAddToCartRateValue ">$172.35</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_2" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">AMS Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue strike">$203.20</span> <span class="productDetailAddToCartRateValue ">$153.20</span> </td> </tr> </tbody> </table> </div> </div> </div> <div class="productDetailProductPrice"> <a href="#" class="productDetailCartBtn" onclick="addToCart('productDetailAddToCartContainer')">Add to cart</a> </div> </div> </div> </div> <!-- Left Column --> <div class="productDetailLeftColumn"> <div class="productDetailImageLoaderContainer"> <div id="productDetailImageLoading" class="productDetailLoadingPanel containedToParent hideContents hidden"> <div> <div class="sp sp-3balls"></div> </div> </div> <img id="productDetailImage" class="productDetailLargeImage" onerror="replaceImageError(this);" src="https://ebus.ams.org/ProductImages/surv-123-s-e-cov-1.jpg" onload="handleImageLoad(this);" title="" style="" alt="Fundamental Algebraic Geometry"> </div> <div class="productDetailImageClickToZoomMessage">Click above image for expanded view</div> </div> <!-- Right Column --> <div class="productDetailRightColumn"> <!-- Product Description --> <div class="productDetailProductDescription"> <div class="productDetailTitle"> <span id="lblProductTitle">Fundamental Algebraic Geometry: Grothendieck’s FGA Explained</span> </div> <div class="productDetailAuthorContainer"> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_0" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Barbara Fantechi')">Barbara Fantechi</a></span> <input id="lblAuthorEditorFullnameHtml_0" type="hidden" value="Barbara Fantechi"/> <span id="lblAuthorEditSpacer_0" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_0" class="productDetailProductDescriptionAuthorAffiliation">SISSA, Trieste, Italy</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_1" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Lothar G&ouml;ttsche')">Lothar Göttsche</a></span> <input id="lblAuthorEditorFullnameHtml_1" type="hidden" value="Lothar G&ouml;ttsche"/> <span id="lblAuthorEditSpacer_1" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_1" class="productDetailProductDescriptionAuthorAffiliation">International Centre for Theoretical Physics, Trieste, Italy</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_2" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Luc Illusie')">Luc Illusie</a></span> <input id="lblAuthorEditorFullnameHtml_2" type="hidden" value="Luc Illusie"/> <span id="lblAuthorEditSpacer_2" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_2" class="productDetailProductDescriptionAuthorAffiliation">Université Paris–Sud, Orsay, France</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_3" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Steven L. Kleiman')">Steven L. Kleiman</a></span> <input id="lblAuthorEditorFullnameHtml_3" type="hidden" value="Steven L. Kleiman"/> <span id="lblAuthorEditSpacer_3" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_3" class="productDetailProductDescriptionAuthorAffiliation">MIT, Cambridge, MA</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_4" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Nitin Nitsure')">Nitin Nitsure</a></span> <input id="lblAuthorEditorFullnameHtml_4" type="hidden" value="Nitin Nitsure"/> <span id="lblAuthorEditSpacer_4" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_4" class="productDetailProductDescriptionAuthorAffiliation">Tata Institute of Fundamental Research, Mumbai, India</span> </div> <div class="productDetailAuthorRow"> <span id="lblAuthorEditorFullname_5" class="productDetailProductDescriptionAuthorName"><a href="#" onclick="navigateToAuthorNameSearch('Angelo Vistoli')">Angelo Vistoli</a></span> <input id="lblAuthorEditorFullnameHtml_5" type="hidden" value="Angelo Vistoli"/> <span id="lblAuthorEditSpacer_5" class="productDetailAuthorEditSpacer">: </span> <span id="lblAuthorEditorAffiliation_5" class="productDetailProductDescriptionAuthorAffiliation">Università di Bologna, Bologna, Italy</span> </div> </div> <div class="productDetailFlagIconContainer"> </div> <div class="productDetailGroupedFormats"> <div class="productDetailTypeContainer "> <div class="productDetailType"> <div class="productDetailBookTypeChoose"> <button ID="btnBookType_0" class="productDetailBookTypeButton active " data-book-type="SOFTCOVER" onclick="selectBookType('SOFTCOVER');">Softcover</button> <button ID="btnBookType_1" class="productDetailBookTypeButton " data-book-type="ELECTRONIC" onclick="selectBookType('ELECTRONIC');">eBook</button> <button ID="btnBookType_2" class="productDetailBookTypeButton bundleItem" data-book-type="BUNDLE_S" onclick="selectBookType('BUNDLE_S');">Softcover + eBook<br><span class='productDetailBundleItemButtonSubtext'>Save 50% on eBook!</span></button> </div> </div> </div> <div class="productDetailCartItemContainer"> <div id="productDetailDIV_0" class="productDetailAddToCartContainer active " data-book-type="SOFTCOVER" data-product-id="12773"> <table> <tbody> <tr class="productDetailAddToCartRow"> <td> <span id="lblISBNType_0" class="productDetailAddToCart">Softcover </span><span class="productDetailAddToCart">ISBN: </span> </td> <td> <span id="lblISBN_0" class="productDetailAddToCartValue">978-0-8218-4245-4</span> </td> </tr> <tr class="productDetailAddToCartRow"> <td> <span class="productDetailAddToCart">Product Code: </span> </td> <td> <span id="lblProductCode_0" class="productDetailAddToCartValue">SURV/123.S</span> </td> </tr> </tbody> </table> <div class="productDetailAddToCartRow productDetailAddToCartRateContainer"> <table> <tbody> <tr id="productDetailAddToCartRateDIV_0" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">List Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$129.00</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_1" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">MAA Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$116.10</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_2" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">AMS Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$103.20</span> </td> </tr> </tbody> </table> </div> </div> <div id="productDetailDIV_1" class="productDetailAddToCartContainer " data-book-type="ELECTRONIC" data-product-id="18794957"> <table> <tbody> <tr class="productDetailAddToCartRow"> <td> <span id="lblISBNType_1" class="productDetailAddToCart">eBook </span><span class="productDetailAddToCart">ISBN: </span> </td> <td> <span id="lblISBN_1" class="productDetailAddToCartValue">978-1-4704-1350-7</span> </td> </tr> <tr class="productDetailAddToCartRow"> <td> <span class="productDetailAddToCart">Product Code: </span> </td> <td> <span id="lblProductCode_1" class="productDetailAddToCartValue">SURV/123.S.E</span> </td> </tr> </tbody> </table> <div class="productDetailAddToCartRow productDetailAddToCartRateContainer"> <table> <tbody> <tr id="productDetailAddToCartRateDIV_0" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">List Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$125.00</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_1" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">MAA Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$112.50</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_2" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">AMS Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue ">$100.00</span> </td> </tr> </tbody> </table> </div> </div> <div id="productDetailDIV_2" class="productDetailAddToCartContainer " data-book-type="BUNDLE_S" data-product-id="1314336555"> <table> <tbody> <tr class="productDetailAddToCartRow"> <td> <span id="lblISBNType_bundle_print_2" class="productDetailAddToCart">Softcover </span><span class="productDetailAddToCart">ISBN: </span> </td> <td> <span id="lblISBN_bundle_print_2" class="productDetailAddToCartValue">978-0-8218-4245-4</span> </td> </tr> <tr class="productDetailAddToCartRow"> <td> <span id="lblISBNType_bundle_electronic_2" class="productDetailAddToCart">eBook </span><span class="productDetailAddToCart">ISBN: </span> </td> <td> <span id="lblISBN_bundle_electronic_2" class="productDetailAddToCartValue">978-1-4704-1350-7</span> </td> </tr> <tr class="productDetailAddToCartRow"> <td> <span class="productDetailAddToCart">Product Code: </span> </td> <td> <span id="lblProductCode_2" class="productDetailAddToCartValue">SURV/123.S.B</span> </td> </tr> </tbody> </table> <div class="productDetailAddToCartRow productDetailAddToCartRateContainer"> <table> <tbody> <tr id="productDetailAddToCartRateDIV_0" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">List Price:</span> </td> <td> <span class="productDetailAddToCartRateValue strike">$254.00</span> <span class="productDetailAddToCartRateValue ">$191.50</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_1" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">MAA Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue strike">$228.60</span> <span class="productDetailAddToCartRateValue ">$172.35</span> </td> </tr> <tr id="productDetailAddToCartRateDIV_2" class="productDetailAddToCartRow "> <td> <span class="productDetailAddToCartRate">AMS Member Price:</span> </td> <td> <span class="productDetailAddToCartRateValue strike">$203.20</span> <span class="productDetailAddToCartRateValue ">$153.20</span> </td> </tr> </tbody> </table> </div> </div> </div> <div class="productDetailProductPrice"> <a href="#" class="productDetailCartBtn" onclick="addToCart('productDetailAddToCartContainer')">Add to cart</a> </div> </div> </div> </div> </div> <div class="productDetailBottomPane"> <div class="productDetailOneColumn"> <ul class="productDetailAccordion productDetailNoList" role="tablist"> <li class="productDetailAccordionListItem"> <div class="productDetailAccordionHeader"> <div class="productDetailAccordionToggleContainer" onclick="toggleDetailMenuItem(this)" onkeypress="handleKeypressForClick(event)" tabindex="0"> <div class="productDetailAccordionLabel">Book Details</div> <div class="productDetailAccordionExpand active"> </div> <div class="productDetailAccordionCollapse"> </div> </div> <div class="productDetailAccordionContent"> <div class="tab-pane active" id="DESCRIPTION" role="tabpanel"> <div class="productDetailDescriptionRow"> <span id="lblSeries" class="productDetailSeries">Mathematical Surveys and Monographs</span> </div> <div class="productDetailDescriptionRow"> <span id="lblSubseries" class="productDetailSubseries"></span> </div> <div class="productDetailDescriptionRow"> <span class="productDetailBookInfoLabel"> Volume: <span id='lblVolume' class='productDetailBookInfoLabel'>123</span>; <span id='lblCopyrightYear' class='productDetailBookInfoLabel'>2005</span><span id='lblPageCount' class='productDetailBookInfoLabel'>; 339 pp</span> </span> </div> <div class="productDetailDescriptionRow"> <span class="productDetailBookInfoLabel"> MSC: <span id="lblMSC" class="productDetailBookInfoLabel">Primary 14; 13; 18</span> </span> </div> <span id="lblDescription" class="productDetailDescription"><p>Alexander Grothendieck's concepts turned out to be astoundingly powerful and productive, truly revolutionizing algebraic geometry. He sketched his new theories in talks given at the Séminaire Bourbaki between 1957 and 1962. He then collected these lectures in a series of articles in <em>Fondements de la géométrie algébrique</em> (commonly known as FGA).</p><p>Much of FGA is now common knowledge. However, some of it is less well known, and only a few geometers are familiar with its full scope. The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), is to fill in the gaps in Grothendieck's very condensed outline of his theories. The four main themes discussed in the book are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The authors present complete proofs of the main results, using newer ideas to promote understanding whenever necessary, and drawing connections to later developments. </p><p>With the main prerequisite being a thorough acquaintance with basic scheme theory, this book is a valuable resource for anyone working in algebraic geometry.</p></span> <div id="productDetailReadershipHeader" class="productDetailReadershipHeader">Readership</div> <span class="productDetailReadership"><p>Graduate students and research mathematicians interested in algebraic geometry.</p></span> </div> </div> </div> </li> <li class="productDetailAccordionListItem"> <div class="productDetailAccordionHeader"> <div class="productDetailAccordionToggleContainer" onclick="toggleDetailMenuItem(this)" onkeypress="handleKeypressForClick(event)" tabindex="0"> <div class="productDetailAccordionLabel">Table of Contents</div> <div class="productDetailAccordionExpand active"> </div> <div class="productDetailAccordionCollapse"> </div> </div> <div class="productDetailAccordionContent"> <div class="tab-pane" id="TOC" role="tabpanel"> <ul id="productDetailTOCContainer" class="productDetailNoList"> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_0" class="productDetailTOC productDetailLevel0">Chapters</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_1" class="productDetailTOC productDetailLevel1">1. Preliminary notions</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_2" class="productDetailTOC productDetailLevel1">2. Contravariant functors</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_3" class="productDetailTOC productDetailLevel1">3. Fibered categories</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_4" class="productDetailTOC productDetailLevel1">4. Stacks</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_5" class="productDetailTOC productDetailLevel1">5. Construction of Hilbert and Quot schemes</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_6" class="productDetailTOC productDetailLevel1">6. Elementary deformation theory</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_7" class="productDetailTOC productDetailLevel1">7. Hilbert schemes of points</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_8" class="productDetailTOC productDetailLevel1">8. Grothendieck’s existence theorem in formal geometry</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_9" class="productDetailTOC productDetailLevel1">9. The Picard scheme</span> </div> </li> </ul> </div> </div> </div> </li> <li class="productDetailAccordionListItem"> <div class="productDetailAccordionHeader"> <div class="productDetailAccordionToggleContainer" onclick="toggleDetailMenuItem(this)" onkeypress="handleKeypressForClick(event)" tabindex="0"> <div class="productDetailAccordionLabel">Additional Material</div> <div class="productDetailAccordionExpand active"> </div> <div class="productDetailAccordionCollapse"> </div> </div> <div class="productDetailAccordionContent"> <div class="tab-pane" id="FILE" role="tabpanel"> <ul id="productDetailFileContainer" class="productDetailNoList"> <li> <div class="productDetailFileRow"> <a id="lblFileDisplay_0" class="productDetailFile" href="https://www.ams.org/publications/authors/books/postpub/surv-123" target="_blank">Supplemental Materials</a> </div> </li> </ul> </div> </div> </div> </li> <li class="productDetailAccordionListItem"> <div class="productDetailAccordionHeader"> <div class="productDetailAccordionToggleContainer" onclick="toggleDetailMenuItem(this)" onkeypress="handleKeypressForClick(event)" tabindex="0"> <div class="productDetailAccordionLabel">Reviews</div> <div class="productDetailAccordionExpand active"> </div> <div class="productDetailAccordionCollapse"> </div> </div> <div class="productDetailAccordionContent"> <div class="tab-pane" id="REVIEWS" role="tabpanel"> <ul id="productDetailReviewContainer" class="productDetailNoList"> <li> <div class="productDetailReviewRow"> <span id="lblReviewText_0" class="productDetailReviewText"><p>All together, this book must be seen as a highly valuable addition to Grotherndieck's fundamental classic FGA, and as a superb contribution to the propagation of his pioneering work just as well. It is fair to say that, for the first time, the wealth of Grotherndieck's FGA has been made accessible to the entire community of algebraic geometers, including non-specialist, young researchers, and seasoned graduate students. The authors have endeavoured to elaborate Grothendieck's ingenious, epoch-making outlines in the greatest possible clarity and detailedness, with complete proofs given throughout...ought to be in the library of anyone using modern algebraic geometry in his (or her) research.</p></span> </div> <div class="productDetailReviewSourceRow"> <span id="lblReviewSource_0" class="productDetailReviewSource"><i>Zentralblatt MATH</i></span> </div> </li> </ul> </div> </div> </div> </li> <li class="productDetailAccordionListItem"> <div class="productDetailAccordionHeader"> <div class="productDetailAccordionToggleContainer" onclick="toggleDetailMenuItem(this)" onkeypress="handleKeypressForClick(event)" tabindex="0"> <div class="productDetailAccordionLabel">Requests</div> <div class="productDetailAccordionExpand active"> </div> <div class="productDetailAccordionCollapse"> </div> </div> <div class="productDetailAccordionContent"> <div class="tab-pane" id="REQUEST" role="tabpanel"> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="requestCopy('REVIEW');" onkeypress="handleKeypressForClick(event)">Review Copy</a></span><span class="productDetailRequestDescription"> – for publishers of book reviews</span></div> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="getPermissions();" onkeypress="handleKeypressForClick(event)">Permission</a></span><span class="productDetailRequestDescription"> – for use of book, eBook, or Journal content</span></div> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="requestCopy('ACCESS');" onkeypress="handleKeypressForClick(event)">Accessibility</a></span><span class="productDetailRequestDescription"> – to request an alternate format of an AMS title</span></div> </div> </div> </div> </li> </ul> </div> <div class="productDetailTwoColumn"> <ul class="productDetailNav productDetailNavTabs productDetailNoList" role="tablist"> <li data-tab-id="DESCRIPTION" class="productDetailAdditionalInfo active" role="presentation" onclick="selectTab('DESCRIPTION');" onkeypress="handleKeypressForClick(event)" tabindex="0">Book Details</li> <li data-tab-id="TOC" role="presentation" class="productDetailAdditionalInfo" onclick="selectTab('TOC');" onkeypress="handleKeypressForClick(event)" tabindex="0">Table of Contents</li> <li data-tab-id="FILE" role="presentation" class="productDetailAdditionalInfo wideTab" onclick="selectTab('FILE');" onkeypress="handleKeypressForClick(event)" tabindex="0">Additional Material</li> <li data-tab-id="REVIEWS" role="presentation" class="productDetailAdditionalInfo" onclick="selectTab('REVIEWS');" onkeypress="handleKeypressForClick(event)" tabindex="0">Reviews</li> <li data-tab-id="REQUEST" role="presentation" class="productDetailAdditionalInfo" onclick="selectTab('REQUEST');" onkeypress="handleKeypressForClick(event)" tabindex="0">Requests</li> </ul> <div class="tab-content productDetailTabContent"> <div class="tab-pane active" id="DESCRIPTION" role="tabpanel"> <div class="productDetailDescriptionRow"> <span id="lblSeries" class="productDetailSeries"><a class='productDetailSeriesLink' href='/SURV'>Mathematical Surveys and Monographs</a></span> </div> <div class="productDetailDescriptionRow"> <span id="lblSubseries" class="productDetailSubseries"></span> </div> <div class="productDetailDescriptionRow"> <span class="productDetailBookInfoLabel"> Volume: <span id='lblVolume' class='productDetailBookInfoLabel'>123</span>; <span id='lblCopyrightYear' class='productDetailBookInfoLabel'>2005</span><span id='lblPageCount' class='productDetailBookInfoLabel'>; 339 pp</span> </span> </div> <div class="productDetailDescriptionRow"> <span class="productDetailBookInfoLabel"> MSC: <span id="lblMSC" class="productDetailBookInfoLabel">Primary 14; 13; 18</span> </span> </div> <span id="lblDescription" class="productDetailDescription"><p>Alexander Grothendieck's concepts turned out to be astoundingly powerful and productive, truly revolutionizing algebraic geometry. He sketched his new theories in talks given at the Séminaire Bourbaki between 1957 and 1962. He then collected these lectures in a series of articles in <em>Fondements de la géométrie algébrique</em> (commonly known as FGA).</p><p>Much of FGA is now common knowledge. However, some of it is less well known, and only a few geometers are familiar with its full scope. The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), is to fill in the gaps in Grothendieck's very condensed outline of his theories. The four main themes discussed in the book are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The authors present complete proofs of the main results, using newer ideas to promote understanding whenever necessary, and drawing connections to later developments. </p><p>With the main prerequisite being a thorough acquaintance with basic scheme theory, this book is a valuable resource for anyone working in algebraic geometry.</p></span> <div id="productDetailReadershipHeader" class="productDetailReadershipHeader">Readership</div> <span class="productDetailReadership"><p>Graduate students and research mathematicians interested in algebraic geometry.</p></span> </div> <div class="tab-pane" id="TOC" role="tabpanel"> <ul id="productDetailTOCContainer" class="productDetailNoList"> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_0" class="productDetailTOC productDetailLevel0">Chapters</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_1" class="productDetailTOC productDetailLevel1">1. Preliminary notions</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_2" class="productDetailTOC productDetailLevel1">2. Contravariant functors</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_3" class="productDetailTOC productDetailLevel1">3. Fibered categories</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_4" class="productDetailTOC productDetailLevel1">4. Stacks</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_5" class="productDetailTOC productDetailLevel1">5. Construction of Hilbert and Quot schemes</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_6" class="productDetailTOC productDetailLevel1">6. Elementary deformation theory</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_7" class="productDetailTOC productDetailLevel1">7. Hilbert schemes of points</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_8" class="productDetailTOC productDetailLevel1">8. Grothendieck’s existence theorem in formal geometry</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_9" class="productDetailTOC productDetailLevel1">9. The Picard scheme</span> </div> </li> </ul> </div> <div class="tab-pane" id="FILE" role="tabpanel"> <ul id="productDetailFileContainer" class="productDetailNoList"> <li> <div class="productDetailFileRow"> <a id="lblFileDisplay_0" class="productDetailFile" href="https://www.ams.org/publications/authors/books/postpub/surv-123" target="_blank">Supplemental Materials</a> </div> </li> </ul> </div> <div class="tab-pane" id="REVIEWS" role="tabpanel"> <ul id="productDetailReviewContainer" class="productDetailNoList"> <li> <div class="productDetailReviewRow"> <span id="lblReviewText_0" class="productDetailReviewText"><p>All together, this book must be seen as a highly valuable addition to Grotherndieck's fundamental classic FGA, and as a superb contribution to the propagation of his pioneering work just as well. It is fair to say that, for the first time, the wealth of Grotherndieck's FGA has been made accessible to the entire community of algebraic geometers, including non-specialist, young researchers, and seasoned graduate students. The authors have endeavoured to elaborate Grothendieck's ingenious, epoch-making outlines in the greatest possible clarity and detailedness, with complete proofs given throughout...ought to be in the library of anyone using modern algebraic geometry in his (or her) research.</p></span> </div> <div class="productDetailReviewSourceRow"> <span id="lblReviewSource_0" class="productDetailReviewSource"><i>Zentralblatt MATH</i></span> </div> </li> </ul> </div> <div class="tab-pane" id="REQUEST" role="tabpanel"> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="requestCopy('REVIEW');" onkeypress="handleKeypressForClick(event)">Review Copy</a></span><span class="productDetailRequestDescription"> – for publishers of book reviews</span></div> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="getPermissions();" onkeypress="handleKeypressForClick(event)">Permission</a></span><span class="productDetailRequestDescription"> – for use of book, eBook, or Journal content</span></div> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="requestCopy('ACCESS');" onkeypress="handleKeypressForClick(event)">Accessibility</a></span><span class="productDetailRequestDescription"> – to request an alternate format of an AMS title</span></div> </div> </div> </div> </div> <div class="productDetailFooterPane"> <a target="_blank"href="https://www.mathjax.org"> <img title="Powered by MathJax" src="https://www.mathjax.org/badge/badge.gif" border="0" alt="Powered by MathJax" /> </a> </div> </div> <div id="productDetailImageZoomWrapper" class="jmodal productDetailImageZoomModal"> <div class="productDetailImageZoomContainer"> <img id="productDetailImageZoom"/> </div> </div> <div id="productDetailGetPermissionsChooserWrapper" class="jmodal productDetailGetPermissionsChooserModal"> <div class="productDetailGetPermissionsInfo"> Please select which format for which you are requesting permissions. </div> <div class="productDetailGetPermissionsChooserContainer"> </div> </div> <input name="__RequestVerificationToken" type="hidden" value="CfDJ8BuSt25sxbNEhWzh7kzUCWWkFye1mNdo7Qe9--c40iG_U5ljo--XE_Yh0mrUC8j3qhs8TVGJtA9bdV4ajuxnhWx3PaVxafnPDB0QQILPA6udGS_K3KB8RzAdfbDiJCCZCNDrr9yb6p6-PNf1TS-Aisg" /> <script type="text/javascript"> $(document).ready(function () { initViewPage(); callGtag("view_item", "div.productDetailAddToCartContainer.active", productDetailObj); }); </script> </main> </div> <footer b-nlceesq935 class="footer text-muted"> <div b-nlceesq935> <a b-nlceesq935 href="https://www.ams.org"><img b-nlceesq935 src="/images/footer-line.png" alt="American Mathematical Society" class="img-responsive" title="" style=""></a> </div> <div b-nlceesq935 class="shareContainer"> <ul b-nlceesq935 class="list-inline shareList"> <li b-nlceesq935><a b-nlceesq935 href="https://www.facebook.com/amermathsoc" title="Follow us on Facebook"><i b-nlceesq935 class="fa-brands fa-facebook-f fa-lg"></i></a></li> <li b-nlceesq935><a b-nlceesq935 href="https://twitter.com/amermathsoc" title="Follow us on X"><i b-nlceesq935 class="fa-brands fa-x-twitter fa-lg"></i></a></li> <li b-nlceesq935><a b-nlceesq935 href="https://www.linkedin.com/company/51001" title="Follow us on LinkedIn"><i b-nlceesq935 class="fa-brands fa-linkedin-in fa-lg"></i></a></li> <li b-nlceesq935><a b-nlceesq935 href="https://www.instagram.com/amermathsoc" title="Follow us on Instagram"><i b-nlceesq935 class="fa-brands fa-instagram fa-lg"></i></a></li> <li b-nlceesq935><a b-nlceesq935 href="https://www.youtube.com/amermathsoc" title="Follow us on YouTube"><i b-nlceesq935 class="fa-brands fa-youtube fa-lg"></i></a></li> </ul> </div> <div b-nlceesq935 class="container"> <p b-nlceesq935><a b-nlceesq935 href="https://www.ams.org/bookstore-email-list" target="_blank" class="btn btn-primary footerBtn">Join Our Email List <span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink" ></span></a></p> <p b-nlceesq935><a b-nlceesq935 href="https://www.ams.org" target="_blank">American Mathematical Society <span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a> · <a b-nlceesq935 href="https://goo.gl/maps/ZvJdkQEC79p" title="Google map 201 Charles Street Providence, Rhode Island" target="_blank">201 Charles Street Providence, Rhode Island 02904-2213 <span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a> · <a b-nlceesq935 href="https://www.ams.org/reach" target="_blank">Contact Us <span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a> </p> <p b-nlceesq935><small b-nlceesq935>AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services marks of the American Mathematical Society and registered in the U.S. Patent and Trademark Office.</small></p> <p b-nlceesq935> © <a b-nlceesq935 href="https://www.ams.org/about-us/copyright" target="_blank">Copyright <span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a> <script> var now = new Date(); document.write(now.getFullYear()); </script>, American Mathematical Society · <a b-nlceesq935 href="https://www.ams.org/about-us/privacy" target="_blank">Privacy Statement <span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a> · <a b-nlceesq935 href="https://www.ams.org/tou">Terms of Use</a> · <a b-nlceesq935 href="https://www.ams.org/accessibility">Accessibility and AMS Online Content</a> · <a b-nlceesq935 href="https://www.ams.org/publications/pubpermissions">Rights and Permissions</a></p> <p b-nlceesq935><a b-nlceesq935 target="_blank" href="/shipping-info">Shipping Information <span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a> · <a b-nlceesq935 target="_blank" href="/international-dist">International Orders <span b-nlceesq935 class="sr-only">(opens in a new tab)</span><span b-nlceesq935 class="extLink"></span></a></p> </div> </footer> <script src="/js/jquery.modal.min.js"></script> </body> </html>