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this.value = '' : true" onblur="this.value == '' ? this.value = 'Search' : true" /></fieldset> </form> <span id='navEnd'></span> </div> <div id="revision"> <html xmlns="http://www.w3.org/1999/xhtml" xmlns:svg="http://www.w3.org/2000/svg" xml:lang="en" lang="en"> <head><meta http-equiv="Content-type" content="application/xhtml+xml;charset=utf-8" /><title>Contents</title></head> <body> <p>This entry is about the text</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Alexander+Grothendieck">Alexander Grothendieck</a>, <em>Éléments de géométrie algébrique</em> (<a href="http://www.numdam.org/numdam-bin/recherche?au=Grothendieck&format=short">numdam</a>)</li> </ul> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#ega'>EGA</a></li> <ul> <li><a href='#list_of_volumes_of_ega'>List of volumes of EGA</a></li> <li><a href='#ega_v_and_beyond'>EGA V and beyond</a></li> </ul> <li><a href='#the_other_series'>The other series:</a></li> <ul> <li><a href='#fga_fondements_de_la_gometrie_algbrique'>FGA (Fondements de la Géometrie Algébrique)</a></li> <li><a href='#sga_sminaire_de_gomtrie_algbrique_du_bois_marie'>SGA (Séminaire de Géométrie Algébrique du Bois Marie)</a></li> </ul> <li><a href='#references'>References</a></li> </ul> </div> <h2 id="ega">EGA</h2> <p>EGA stands for <em>Éléments de géométrie algébrique</em> (Elements of algebraic geometry), which was written by <a class="existingWikiWord" href="/nlab/show/Alexandre+Grothendieck">Alexandre Grothendieck</a> and co-edited with <a class="existingWikiWord" href="/nlab/show/Jean+Dieudonne">Jean Dieudonné</a>. These volumes (and a list is given below) were among his many works attempting to build the foundations for <a class="existingWikiWord" href="/nlab/show/algebraic+geometry">algebraic geometry</a> in the language of <a class="existingWikiWord" href="/nlab/show/schemes">schemes</a>. They were preceded by <a class="existingWikiWord" href="/nlab/show/FGA">FGA</a> and were followed up by the SGA, more details of these can be found below.</p> <p>The published part of <em>EGA</em> is in Publ. IHÉS, now free online at <a href="http://www.numdam.org/numdam-bin/recherche?au=Grothendieck&format=short">numdam</a> (detailed links to chapters, and their contents will be added here later, see also below for a list of the volumes in the series). We plan to list here the grand plan and some remarks and links.</p> <h3 id="list_of_volumes_of_ega">List of volumes of EGA</h3> <p>Note that there is a chapter 0 that continues at the beginning of each chapter, establishing preliminaries from <a class="existingWikiWord" href="/nlab/show/topology">topology</a>, <a class="existingWikiWord" href="/nlab/show/category+theory">category theory</a>, <a class="existingWikiWord" href="/nlab/show/commutative+algebra">commutative algebra</a>, <a class="existingWikiWord" href="/nlab/show/homological+algebra">homological algebra</a>, etc.</p> <ul> <li> <p>I. Le langage des schémas, Inst. Hautes Études Sci. Publ. Math. 4 (1960), 5–228. Ch. 0.§1–7 ; Ch I.§1–10.</p> </li> <li> <p>II. Étude globale élémentaire de quelques classes de morphismes, Inst. Hautes Études Sci. Publ. Math. 8 (1961), 5–222. Ch. II.§1–8.</p> </li> <li> <p>III_1. Étude cohomologique des faisceaux cohérents (Première partie) Inst. Hautes Études Sci. Publ. Math. 11 (1961), 5–167. Ch. 0.§8–13 ; Ch.III.§1–5.</p> </li> <li> <p>III_2. Étude cohomologique des faisceaux cohérents (Seconde partie) Inst. Hautes Études Sci. Publ. Math. 17 (1963), 5–91. Ch. III .§6–7.</p> </li> <li> <p>IV_1. Étude locale des schémas et des morphismes de schémas (Première partie) Inst. Hautes Études Sci. Publ. Math. 20 (1964), 5–259. Ch.0.§14–23 ; Ch. IV.§1.</p> </li> <li> <p>IV_2. Étude locale des schémas et des morphismes de schémas (Seconde partie) Inst. Hautes Études Sci. Publ. Math. 24 (1965), 5–231. Ch. IV2.§2–7 .</p> </li> <li> <p>IV_3. Étude locale des schémas et des morphismes de schémas (Troisième partie) Inst. Hautes Études Sci. Publ. Math. 28 (1966), 5–255. Ch. IV.§8–15 (<a href="http://www.numdam.org/item/PMIHES_1966__28__5_0/">numdam:PMIHES_1966__28__5_0/</a>)</p> </li> <li> <p>IV_4. Étude locale des schémas et des morphismes de schémas (Quatrième partie) Inst. Hautes Études Sci. Publ. Math. 32 (1967), 5–361. Ch.IV.§16–21 (<a href="http://www.numdam.org/item/PMIHES_1967__32__5_0">numdam:PMIHES_1967__32__5_0</a>)</p> </li> </ul> <p>There was a second edition of EGA I:</p> <ul> <li>I. Le langage des schémas. (2nd ed.) Grundlehren der Mathematischen Wissenschaften (1971). 166. Springer-Verlag.</li> </ul> <p>In this edition, the term “prescheme” (now outdated but used in the first edition for what we now call schemes) was replaced by “scheme”, and the term “scheme” became <a class="existingWikiWord" href="/nlab/show/separated+scheme">separated scheme</a>. Also, there was a transition to the <a class="existingWikiWord" href="/nlab/show/functor+of+points">functor of points</a> approach to scheme theory.</p> <h3 id="ega_v_and_beyond">EGA V and beyond</h3> <p>EGA was never completed. The listed volumes I-IV are just a part of the original plan. Grothendieck outlined what was meant to be in chapters V-VII, at least, and some handwritten prenotes existed for a small part of those. See e.g. these prenotes for some parts of <a href="http://www.jmilne.org/math/Documents/EGA-V.pdf">EGA V</a>.</p> <p><a href="http://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique">Wikipedia</a> lists the titles of planned chapters I-XIII.</p> <h2 id="the_other_series">The other series:</h2> <h3 id="fga_fondements_de_la_gometrie_algbrique">FGA (Fondements de la Géometrie Algébrique)</h3> <p>The earliest of the series is <em><a class="existingWikiWord" href="/nlab/show/FGA">FGA</a></em> written alone at the end of the 1950s; it is sort of quick outline of the theory and some deep results with proofs at the beginning of the period of the development of <span class="newWikiWord">scheme theory<a href="/nlab/new/scheme+theory">?</a></span>. A modern version of the material in <a class="existingWikiWord" href="/nlab/show/FGA">FGA</a> appeared as a book <a class="existingWikiWord" href="/nlab/show/FGA+explained">FGA explained</a> (ICTP, Trieste 2003–2005). The original is available <a href="http://www.math.jussieu.fr/~leila/grothendieckcircle/FGA.pdf">here</a>.</p> <h3 id="sga_sminaire_de_gomtrie_algbrique_du_bois_marie">SGA (Séminaire de Géométrie Algébrique du Bois Marie)</h3> <p>(Bois Marie is the name of an area of woodland at Bures-sur-Yvette, where the <a class="existingWikiWord" href="/nlab/show/math+institutions">IHÉS</a> is situated.)</p> <p><em>SGA</em> consists of the writeups of seminars at IHÉS lead by Grothendieck; the work of the members of the seminar under the guidance of Grothendieck are included. In <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>lab we have pages on <a class="existingWikiWord" href="/nlab/show/SGA1">SGA1</a>, and <a class="existingWikiWord" href="/nlab/show/SGA4">SGA4</a>.</p> <p>The <a href="http://en.wikipedia.org/wiki/S%C3%A9minaire_de_G%C3%A9om%C3%A9trie_Alg%C3%A9brique_du_Bois_Marie">Wikipedia entry</a> lists all of the seminars.</p> <p><a class="existingWikiWord" href="/nlab/show/Pierre+Deligne">Pierre Deligne</a> edited a supplementary volume <em>SGA <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>4</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding="application/x-tex">4\frac{1}{2}</annotation></semantics></math></em> comprisings parts of <span class="newWikiWord">SGA5<a href="/nlab/new/SGA5">?</a></span>, his own articles proving new results and some substantially rewritten and expanded material exposed in less satisfactory form in SGA5 (these results were used for his proof of the <a class="existingWikiWord" href="/nlab/show/Weil+conjecture"> Weil conjectures</a> which appeared before SGA5).</p> <p>An ongoing project aims to retype the SGA volumes in TeX. So far the following volumes have been retyped:</p> <ul> <li> <p><a href="http://arxiv.org/abs/math/0206203">SGA 1</a> - Edited by B. Edixhoven, 2004</p> </li> <li> <p><a href="http://arxiv.org/abs/math/0511279">SGA 2</a> - Edited by Y. Laszlo, 2004</p> </li> <li> <p><a href="http://webusers.imj-prg.fr/~patrick.polo/SGA3/">SGA 3</a> - Edited by P. Gilles and P. Polo, 2011</p> </li> <li> <p>SGA 4 - Edited by Y. Laszlo.</p> <p><a href="http://www.math.polytechnique.fr/~laszlo/sga4/SGA4-1/sga41.pdf">Part 1</a>,</p> <p><a href="http://www.math.polytechnique.fr/~laszlo/sga4/SGA4-2/sga42.pdf">Part 2</a>,</p> <p><a href="http://www.math.polytechnique.fr/~laszlo/sga4/SGA4-3/sga43.pdf">Part 3</a>.</p> </li> <li> <p><a href="https://github.com/dkmiller/sga4.5">SGA <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mn>4</mn><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">4{1\over2}</annotation></semantics></math></a> - Edited by Daniel Miller.</p> </li> </ul> <p>See also:</p> <ul> <li><a href="http://fabrice.orgogozo.perso.math.cnrs.fr/SGA4/index.html">SGA 4</a> Edited by F. Orgogozo</li> </ul> <h2 id="references">References</h2> <p>There are Wikipedia entries</p> <ul> <li> <p>Wikipedia, <a href="http://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique">Éléments de géométrie algébrique</a></p> </li> <li> <p>Wikipedia, <a href="http://en.wikipedia.org/wiki/S%C3%A9minaire_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique">Séminaire de Géométrie Algébrique du Bois Marie</a></p> </li> <li> <p>Wikipedia, <a href="http://en.wikipedia.org/wiki/Fondements_de_la_G%C3%A9ometrie_Alg%C3%A9brique">Fondements de la Géometrie Algébrique</a></p> </li> </ul> <p>EGA and the other published texts of Grothendieck are available from</p> <ul> <li><span class="newWikiWord">Grothendieck Circle<a href="/nlab/new/Grothendieck+Circle">?</a></span>, <a href="http://www.math.jussieu.fr/~leila/grothendieckcircle/pubtexts.php">Scans of published texts</a>.</li> </ul> <p>and some of the EGA and SGA links are at this <a href="http://www.cmls.polytechnique.fr/perso/chambert/DJVU/index.html">html</a>.</p> <p>David Madore has prepared a detailed table of contents of EGA:</p> <ul> <li><a href="https://math.berkeley.edu/~mhaiman/math256-fall13-spring14/EGA-contents.pdf">Detailed table of contents of EGA</a></li> </ul> <p>A translated table of contents has been prepared by Mark Haiman, available at</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Mark+Haiman">Mark Haiman</a>, <a href="http://math.berkeley.edu/~mhaiman/math256/EGA-contents.pdf">English translation of table of contents of EGA</a></li> </ul> <p>along with synopsises, in English, of many sections at</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Mark+Haiman">Mark Haiman</a>, <a href="https://math.berkeley.edu/~mhaiman/math256-fall18-spring19/#ega">English synopsises of most of EGA I and II</a></li> </ul> <p>There is an ongoing open-source project to translate EGA into English:</p> <ul> <li><a href="https://github.com/ryankeleti/ega">English translation of EGA I, and partial translations of the rest</a></li> </ul> <p>Daniel Murfet has written notes for parts of EGA, see</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Daniel+Murfet">Daniel Murfet</a>, <a href="http://therisingsea.org/?page_id=3">The Rising Sea</a></li> </ul> <p>Project of classification and transcription</p> <ul> <li><a href="https://agrothendieck.github.io/SGAEGAFGA.html">SGA, EGA, FGA</a> By Mateo Carmona</li> </ul> <p>For an essay on content of EGA (about 50 years after the publication) see</p> <ul> <li>U. Görtz, <em>Classics revisited: Éléments de Géométrie Algébrique</em>, Jahresbericht der Deutschen Mathematiker-Vereinigung <strong>120</strong>, 235–290 (2018) <a href="https://doi.org/10.1365/s13291-018-0181-1">doi</a></li> </ul> <div class="property">category: <a class="category_link" href="/nlab/all_pages/reference">reference</a></div></body></html> </div> <div class="revisedby"> <p> Last revised on November 15, 2023 at 04:32:48. 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