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searchaux" style="display:none">1960–67 foundational treatise on algebraic geometry by Alexander Grothendieck</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox vcard"><caption class="infobox-title" style="font-size:125%; font-style:italic; padding-bottom:0.2em;">Éléments de géométrie algébrique <span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique&rft.author=%5B%5BAlexander+Grothendieck%5D%5D+and+%5B%5BJean+Dieudonn%C3%A9%5D%5D&rft.date=1960%26ndash%3B1967&rft.pub=%5B%5BInstitut+des+Hautes+%C3%89tudes+Scientifiques%5D%5D"></span></caption><tbody><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique_title_page.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/4/4d/%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique_title_page.jpg/200px-%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique_title_page.jpg" decoding="async" width="200" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/4/4d/%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique_title_page.jpg 1.5x" data-file-width="282" data-file-height="354" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Author</th><td class="infobox-data"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Alexander Grothendieck</a> and <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Jean Dieudonné</a></td></tr><tr><th scope="row" class="infobox-label">Language</th><td class="infobox-data">French</td></tr><tr><th scope="row" class="infobox-label">Subject</th><td class="infobox-data"><a href="/wiki/Algebraic_geometry" title="Algebraic geometry">Algebraic geometry</a></td></tr><tr><th scope="row" class="infobox-label">Publisher</th><td class="infobox-data"><a href="/wiki/Institut_des_Hautes_%C3%89tudes_Scientifiques" title="Institut des Hautes Études Scientifiques">Institut des Hautes Études Scientifiques</a></td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Publication date</div></th><td class="infobox-data">1960–1967</td></tr></tbody></table> <p>The <b><span title="French-language text"><i lang="fr">Éléments de géométrie algébrique</i></span></b> (<i><b>EGA</b></i>; from <a href="/wiki/French_language" title="French language">French</a>: "Elements of <a href="/wiki/Algebraic_geometry" title="Algebraic geometry">Algebraic Geometry</a>") by <a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Alexander Grothendieck</a> (assisted by <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Jean Dieudonné</a>) is a rigorous treatise on <a href="/wiki/Algebraic_geometry" title="Algebraic geometry">algebraic geometry</a> that was published (in eight parts or <a href="/wiki/Fascicle_(book)" class="mw-redirect" title="Fascicle (book)">fascicles</a>) from 1960 through 1967 by the <span title="French-language text"><i lang="fr"><a href="/wiki/Institut_des_Hautes_%C3%89tudes_Scientifiques" title="Institut des Hautes Études Scientifiques">Institut des Hautes Études Scientifiques</a></i></span>. In it, Grothendieck established systematic foundations of algebraic geometry, building upon the concept of <a href="/wiki/Scheme_(mathematics)" title="Scheme (mathematics)">schemes</a>, which he defined. The work is now considered the foundation and basic reference of modern algebraic geometry. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Editions">Editions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique&action=edit&section=1" title="Edit section: Editions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Initially thirteen chapters were planned, but only the first four (making a total of approximately 1500 pages) were published. Much of the material which would have been found in the following chapters can be found, in a less polished form, in the <i><a href="/wiki/S%C3%A9minaire_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique" class="mw-redirect" title="Séminaire de géométrie algébrique">Séminaire de géométrie algébrique</a></i> (known as <i>SGA</i>). Indeed, as explained by Grothendieck in the preface of the published version of <i>SGA</i>, by 1970 it had become clear that incorporating all of the planned material in <i>EGA</i> would require significant changes in the earlier chapters already published, and that therefore the prospects of completing <i>EGA</i> in the near term were limited. An obvious example is provided by <a href="/wiki/Derived_category" title="Derived category">derived categories</a>, which became an indispensable tool in the later <i>SGA</i> volumes, but was not yet used in <i>EGA III</i> as the theory was not yet developed at the time. Considerable effort was therefore spent to bring the published <i>SGA</i> volumes to a high degree of completeness and rigour. Before work on the treatise was abandoned, there were plans in 1966–67 to expand the group of authors to include Grothendieck's students <a href="/wiki/Pierre_Deligne" title="Pierre Deligne">Pierre Deligne</a> and <a href="/wiki/Michel_Raynaud" title="Michel Raynaud">Michel Raynaud</a>, as evidenced by published correspondence between Grothendieck and <a href="/wiki/David_Mumford" title="David Mumford">David Mumford</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Grothendieck's letter of 4 November 1966 to Mumford also indicates that the second-edition revised structure was in place by that time, with Chapter VIII already intended to cover the <a href="/wiki/Picard_group#Picard_scheme" title="Picard group">Picard scheme</a>. In that letter he estimated that at the pace of writing up to that point, the following four chapters (V to VIII) would have taken eight years to complete, indicating an intended length comparable to the first four chapters, which had been in preparation for about eight years at the time. </p><p>Grothendieck nevertheless wrote a revised version of <i>EGA I</i> which was published by <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer-Verlag</a>. It updates the terminology, replacing "prescheme" by "scheme" and "scheme" by "separated scheme", and heavily emphasizes the use of <a href="/wiki/Representable_functor" title="Representable functor">representable functors</a>. The new preface of the second edition also includes a slightly revised plan of the complete treatise, now divided into twelve chapters. </p><p>Grothendieck's <i>EGA V</i> which deals with <a href="/wiki/Theorem_of_Bertini" title="Theorem of Bertini">Bertini</a> type theorems is to some extent available from <a rel="nofollow" class="external text" href="http://www.grothendieckcircle.org/">the Grothendieck Circle website</a>. <i>Monografie Matematyczne</i> in Poland has accepted this volume for publication, but the editing process is quite slow (as of 2010). <a href="/wiki/James_Milne_(mathematician)" title="James Milne (mathematician)">James Milne</a> has preserved some of the original Grothendieck notes and a translation of them into English. They may be available from his websites connected with the <a href="/wiki/University_of_Michigan_in_Ann_Arbor" class="mw-redirect" title="University of Michigan in Ann Arbor">University of Michigan in Ann Arbor</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Chapters">Chapters</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique&action=edit&section=2" title="Edit section: Chapters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following table lays out the original and revised plan of the treatise and indicates where (in <i>SGA</i> or elsewhere) the topics intended for the later, unpublished chapters were treated by Grothendieck and his collaborators. </p> <table class="wikitable"> <tbody><tr> <th># </th> <th width="27%">First edition </th> <th width="27%">Second edition </th> <th>Comments </th></tr> <tr> <td>I </td> <td><b>Le langage des schémas</b> </td> <td><b>Le langage des schémas</b> </td> <td>Second edition brings in certain schemes representing functors such as <a href="/wiki/Grassmannian" title="Grassmannian">Grassmannians</a>, presumably from intended Chapter V of the first edition. In addition, the contents of Section 1 of Chapter IV of first edition was moved to Chapter I in the second edition. </td></tr> <tr> <td>II </td> <td><b>Étude globale élémentaire de quelques classes de morphismes</b> </td> <td>Étude globale élémentaire de quelques classes de morphismes </td> <td>First edition complete, second edition did not appear. </td></tr> <tr> <td>III </td> <td><b>Étude cohomologique des faisceaux cohérents</b> </td> <td>Cohomologie des Faisceaux algébriques cohérents. Applications. </td> <td>First edition complete except for last four sections, intended for publication after Chapter IV: elementary projective duality, local cohomology and its relation to projective cohomology, and Picard groups (all but projective duality treated in <i>SGA II</i>). </td></tr> <tr> <td>IV </td> <td><b>Étude locale des schémas et des morphismes de schémas</b> </td> <td>Étude locale des schémas et des morphismes de schémas </td> <td>First edition essentially complete; some changes made in last sections; the section on hyperplane sections made into the new Chapter V of second edition (draft exists) </td></tr> <tr> <td>V </td> <td>Procédés élémentaires de construction de schémas </td> <td>Complements sur les morphismes projectifs </td> <td>Did not appear. Some elementary constructions of schemes apparently intended for first edition appear in Chapter I of second edition. The existing draft of Chapter V corresponds to the second edition plan. It includes also expanded treatment of some material from <i>SGA VII</i>. </td></tr> <tr> <td>VI </td> <td>Technique de descente.<br /> Méthode générale de construction des schémas </td> <td>Techniques de construction de schémas </td> <td>Did not appear. <a href="/wiki/Descent_theory" class="mw-redirect" title="Descent theory">Descent theory</a> and related construction techniques summarised by Grothendieck in <i><a href="/wiki/Fondements_de_la_G%C3%A9ometrie_Alg%C3%A9brique" title="Fondements de la Géometrie Algébrique">FGA</a></i>. By 1968 the plan had evolved to treat <a href="/wiki/Algebraic_space" title="Algebraic space">algebraic spaces</a> and <a href="/wiki/Algebraic_stack" title="Algebraic stack">algebraic stacks</a>. </td></tr> <tr> <td>VII </td> <td>Schémas de groupes, espaces fibrés principaux </td> <td>Schémas en groupes, espaces fibrés principaux </td> <td>Did not appear. Treated in detail in <i>SGA III</i>. </td></tr> <tr> <td>VIII </td> <td>Étude différentielle des espaces fibrés </td> <td>Le schéma de Picard </td> <td>Did not appear. Material apparently intended for first edition can be found in <i>SGA III</i>, construction and results on Picard scheme are summarised in <i><a href="/wiki/Fondements_de_la_G%C3%A9ometrie_Alg%C3%A9brique" title="Fondements de la Géometrie Algébrique">FGA</a></i>. </td></tr> <tr> <td>IX </td> <td>Le groupe fondamental </td> <td>Le groupe fondamental </td> <td>Did not appear. Treated in detail in <i>SGA I</i>. </td></tr> <tr> <td>X </td> <td>Résidus et dualité </td> <td>Résidus et dualité </td> <td>Did not appear. Treated in detail in Hartshorne's edition of Grothendieck's notes "Residues and duality" </td></tr> <tr> <td>XI </td> <td>Théorie d'intersection, classes de Chern, théorème de Riemann-Roch </td> <td>Théorie d'intersection, classes de Chern, théorème de Riemann-Roch </td> <td>Did not appear. Treated in detail in <i>SGA VI</i>. </td></tr> <tr> <td>XII </td> <td>Schémas abéliens et schémas de Picard </td> <td>Cohomologie étale des schémas </td> <td>Did not appear. Étale cohomology treated in detail in <i>SGA IV</i>, <i>SGA V</i>. </td></tr> <tr> <td>XIII </td> <td>Cohomologie de Weil </td> <td>none </td> <td>Intended to cover étale cohomology in the first edition. </td></tr></tbody></table> <p>In addition to the actual chapters, an extensive "Chapter 0" on various preliminaries was divided between the volumes in which the treatise appeared. Topics treated range from <a href="/wiki/Category_theory" title="Category theory">category theory</a>, <a href="/wiki/Sheaf_(mathematics)" title="Sheaf (mathematics)">sheaf theory</a> and <a href="/wiki/General_topology" title="General topology">general topology</a> to <a href="/wiki/Commutative_algebra" title="Commutative algebra">commutative algebra</a> and <a href="/wiki/Homological_algebra" title="Homological algebra">homological algebra</a>. The longest part of Chapter 0, attached to Chapter IV, is more than 200 pages. </p><p>Grothendieck never gave permission for the 2nd edition of <i>EGA I</i> to be republished, so copies are rare but found in many libraries. The work on <i>EGA</i> was finally disrupted by Grothendieck's departure first from <a href="/wiki/IH%C3%89S" class="mw-redirect" title="IHÉS">IHÉS</a> in 1970 and soon afterwards from the mathematical establishment altogether. Grothendieck's incomplete notes on <i>EGA V</i> can be found at <a rel="nofollow" class="external text" href="http://www.grothendieckcircle.org/">Grothendieck Circle</a>. </p><p>In historical terms, the development of the <i>EGA</i> approach set the seal on the application of <a href="/wiki/Sheaf_theory" class="mw-redirect" title="Sheaf theory">sheaf theory</a> to algebraic geometry, set in motion by <a href="/wiki/Jean-Pierre_Serre" title="Jean-Pierre Serre">Serre</a>'s basic paper <i><a href="/wiki/Faisceaux_alg%C3%A9briques_coh%C3%A9rents" class="mw-redirect" title="Faisceaux algébriques cohérents">FAC</a></i>. It also contained the first complete exposition of the algebraic approach to differential calculus, via principal parts. The foundational unification it proposed (see for example <a href="/wiki/Unifying_theories_in_mathematics" title="Unifying theories in mathematics">unifying theories in mathematics</a>) has stood the test of time. </p><p><i>EGA</i> has been scanned by <a href="/w/index.php?title=NUMDAM&action=edit&redlink=1" class="new" title="NUMDAM (page does not exist)">NUMDAM</a> and is available at <a rel="nofollow" class="external text" href="http://www.numdam.org">their website</a> under "Publications mathématiques de l'IHÉS", volumes 4 (EGAI), 8 (EGAII), 11 (EGAIII.1re), 17 (EGAIII.2e), 20 (EGAIV.1re), 24 (EGAIV.2e), 28 (EGAIV.3e) and 32 (EGAIV.4e). </p> <div class="mw-heading mw-heading2"><h2 id="Bibliographic_information">Bibliographic information</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique&action=edit&section=3" title="Edit section: Bibliographic information"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFGrothendieckDieudonné1971" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck, Alexandre</a>; <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Dieudonné, Jean</a> (1971). <i>Éléments de géométrie algébrique: I. Le langage des schémas</i>. Grundlehren der Mathematischen Wissenschaften (in French). Vol. 166 (2nd ed.). Berlin; New York: <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer-Verlag</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-05113-8" title="Special:BookSources/978-3-540-05113-8"><bdi>978-3-540-05113-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%3A+I.+Le+langage+des+sch%C3%A9mas&rft.place=Berlin%3B+New+York&rft.series=Grundlehren+der+Mathematischen+Wissenschaften&rft.edition=2nd&rft.pub=Springer-Verlag&rft.date=1971&rft.isbn=978-3-540-05113-8&rft.aulast=Grothendieck&rft.aufirst=Alexandre&rft.au=Dieudonn%C3%A9%2C+Jean&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrothendieckDieudonné1960" class="citation journal cs1"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck, Alexandre</a>; <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Dieudonné, Jean</a> (1960). <a rel="nofollow" class="external text" href="http://www.numdam.org/item/PMIHES_1960__4__5_0">"Éléments de géométrie algébrique: I. Le langage des schémas"</a>. <i><a href="/wiki/Publications_Math%C3%A9matiques_de_l%27IH%C3%89S" title="Publications Mathématiques de l'IHÉS">Publications Mathématiques de l'IHÉS</a></i>. <b>4</b>: 5–228. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02684778">10.1007/bf02684778</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0217083">0217083</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+Math%C3%A9matiques+de+l%27IH%C3%89S&rft.atitle=%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%3A+I.+Le+langage+des+sch%C3%A9mas&rft.volume=4&rft.pages=5-228&rft.date=1960&rft_id=info%3Adoi%2F10.1007%2Fbf02684778&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0217083%23id-name%3DMR&rft.aulast=Grothendieck&rft.aufirst=Alexandre&rft.au=Dieudonn%C3%A9%2C+Jean&rft_id=http%3A%2F%2Fwww.numdam.org%2Fitem%2FPMIHES_1960__4__5_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrothendieckDieudonné1961" class="citation journal cs1"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck, Alexandre</a>; <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Dieudonné, Jean</a> (1961). <a rel="nofollow" class="external text" href="http://www.numdam.org/item/PMIHES_1961__8__5_0">"Éléments de géométrie algébrique: II. Étude globale élémentaire de quelques classes de morphismes"</a>. <i><a href="/wiki/Publications_Math%C3%A9matiques_de_l%27IH%C3%89S" title="Publications Mathématiques de l'IHÉS">Publications Mathématiques de l'IHÉS</a></i>. <b>8</b>: 5–222. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02699291">10.1007/bf02699291</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0217084">0217084</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+Math%C3%A9matiques+de+l%27IH%C3%89S&rft.atitle=%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%3A+II.+%C3%89tude+globale+%C3%A9l%C3%A9mentaire+de+quelques+classes+de+morphismes&rft.volume=8&rft.pages=5-222&rft.date=1961&rft_id=info%3Adoi%2F10.1007%2Fbf02699291&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0217084%23id-name%3DMR&rft.aulast=Grothendieck&rft.aufirst=Alexandre&rft.au=Dieudonn%C3%A9%2C+Jean&rft_id=http%3A%2F%2Fwww.numdam.org%2Fitem%2FPMIHES_1961__8__5_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrothendieckDieudonné1961" class="citation journal cs1"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck, Alexandre</a>; <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Dieudonné, Jean</a> (1961). <a rel="nofollow" class="external text" href="http://www.numdam.org/item/PMIHES_1961__11__5_0">"Eléments de géométrie algébrique: III. Étude cohomologique des faisceaux cohérents, Première partie"</a>. <i><a href="/wiki/Publications_Math%C3%A9matiques_de_l%27IH%C3%89S" title="Publications Mathématiques de l'IHÉS">Publications Mathématiques de l'IHÉS</a></i>. <b>11</b>: 5–167. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02684274">10.1007/bf02684274</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0217085">0217085</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+Math%C3%A9matiques+de+l%27IH%C3%89S&rft.atitle=El%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%3A+III.+%C3%89tude+cohomologique+des+faisceaux+coh%C3%A9rents%2C+Premi%C3%A8re+partie&rft.volume=11&rft.pages=5-167&rft.date=1961&rft_id=info%3Adoi%2F10.1007%2Fbf02684274&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0217085%23id-name%3DMR&rft.aulast=Grothendieck&rft.aufirst=Alexandre&rft.au=Dieudonn%C3%A9%2C+Jean&rft_id=http%3A%2F%2Fwww.numdam.org%2Fitem%2FPMIHES_1961__11__5_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrothendieckDieudonné1963" class="citation journal cs1"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck, Alexandre</a>; <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Dieudonné, Jean</a> (1963). <a rel="nofollow" class="external text" href="http://www.numdam.org/item/PMIHES_1963__17__5_0">"Éléments de géométrie algébrique: III. Étude cohomologique des faisceaux cohérents, Seconde partie"</a>. <i><a href="/wiki/Publications_Math%C3%A9matiques_de_l%27IH%C3%89S" title="Publications Mathématiques de l'IHÉS">Publications Mathématiques de l'IHÉS</a></i>. <b>17</b>: 5–91. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02684890">10.1007/bf02684890</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0163911">0163911</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+Math%C3%A9matiques+de+l%27IH%C3%89S&rft.atitle=%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%3A+III.+%C3%89tude+cohomologique+des+faisceaux+coh%C3%A9rents%2C+Seconde+partie&rft.volume=17&rft.pages=5-91&rft.date=1963&rft_id=info%3Adoi%2F10.1007%2Fbf02684890&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0163911%23id-name%3DMR&rft.aulast=Grothendieck&rft.aufirst=Alexandre&rft.au=Dieudonn%C3%A9%2C+Jean&rft_id=http%3A%2F%2Fwww.numdam.org%2Fitem%2FPMIHES_1963__17__5_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrothendieckDieudonné1964" class="citation journal cs1"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck, Alexandre</a>; <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Dieudonné, Jean</a> (1964). <a rel="nofollow" class="external text" href="http://www.numdam.org/item/PMIHES_1964__20__5_0">"Éléments de géométrie algébrique: IV. Étude locale des schémas et des morphismes de schémas, Première partie"</a>. <i><a href="/wiki/Publications_Math%C3%A9matiques_de_l%27IH%C3%89S" title="Publications Mathématiques de l'IHÉS">Publications Mathématiques de l'IHÉS</a></i>. <b>20</b>: 5–259. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02684747">10.1007/bf02684747</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0173675">0173675</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+Math%C3%A9matiques+de+l%27IH%C3%89S&rft.atitle=%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%3A+IV.+%C3%89tude+locale+des+sch%C3%A9mas+et+des+morphismes+de+sch%C3%A9mas%2C+Premi%C3%A8re+partie&rft.volume=20&rft.pages=5-259&rft.date=1964&rft_id=info%3Adoi%2F10.1007%2Fbf02684747&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0173675%23id-name%3DMR&rft.aulast=Grothendieck&rft.aufirst=Alexandre&rft.au=Dieudonn%C3%A9%2C+Jean&rft_id=http%3A%2F%2Fwww.numdam.org%2Fitem%2FPMIHES_1964__20__5_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrothendieckDieudonné1965" class="citation journal cs1"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck, Alexandre</a>; <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Dieudonné, Jean</a> (1965). <a rel="nofollow" class="external text" href="http://www.numdam.org/articles/PMIHES_1965__24__5_0">"Éléments de géométrie algébrique: IV. Étude locale des schémas et des morphismes de schémas, Seconde partie"</a>. <i><a href="/wiki/Publications_Math%C3%A9matiques_de_l%27IH%C3%89S" title="Publications Mathématiques de l'IHÉS">Publications Mathématiques de l'IHÉS</a></i>. <b>24</b>: 5–231. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02684322">10.1007/bf02684322</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0199181">0199181</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+Math%C3%A9matiques+de+l%27IH%C3%89S&rft.atitle=%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%3A+IV.+%C3%89tude+locale+des+sch%C3%A9mas+et+des+morphismes+de+sch%C3%A9mas%2C+Seconde+partie&rft.volume=24&rft.pages=5-231&rft.date=1965&rft_id=info%3Adoi%2F10.1007%2Fbf02684322&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0199181%23id-name%3DMR&rft.aulast=Grothendieck&rft.aufirst=Alexandre&rft.au=Dieudonn%C3%A9%2C+Jean&rft_id=http%3A%2F%2Fwww.numdam.org%2Farticles%2FPMIHES_1965__24__5_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrothendieckDieudonné1966" class="citation journal cs1"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck, Alexandre</a>; <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Dieudonné, Jean</a> (1966). <a rel="nofollow" class="external text" href="http://www.numdam.org/articles/PMIHES_1966__28__5_0">"Éléments de géométrie algébrique: IV. Étude locale des schémas et des morphismes de schémas, Troisième partie"</a>. <i><a href="/wiki/Publications_Math%C3%A9matiques_de_l%27IH%C3%89S" title="Publications Mathématiques de l'IHÉS">Publications Mathématiques de l'IHÉS</a></i>. <b>28</b>: 5–255. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02684343">10.1007/bf02684343</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0217086">0217086</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+Math%C3%A9matiques+de+l%27IH%C3%89S&rft.atitle=%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%3A+IV.+%C3%89tude+locale+des+sch%C3%A9mas+et+des+morphismes+de+sch%C3%A9mas%2C+Troisi%C3%A8me+partie&rft.volume=28&rft.pages=5-255&rft.date=1966&rft_id=info%3Adoi%2F10.1007%2Fbf02684343&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0217086%23id-name%3DMR&rft.aulast=Grothendieck&rft.aufirst=Alexandre&rft.au=Dieudonn%C3%A9%2C+Jean&rft_id=http%3A%2F%2Fwww.numdam.org%2Farticles%2FPMIHES_1966__28__5_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrothendieckDieudonné1967" class="citation journal cs1"><a href="/wiki/Alexander_Grothendieck" title="Alexander Grothendieck">Grothendieck, Alexandre</a>; <a href="/wiki/Jean_Dieudonn%C3%A9" title="Jean Dieudonné">Dieudonné, Jean</a> (1967). <a rel="nofollow" class="external text" href="http://www.numdam.org/articles/PMIHES_1967__32__5_0">"Éléments de géométrie algébrique: IV. Étude locale des schémas et des morphismes de schémas, Quatrième partie"</a>. <i><a href="/wiki/Publications_Math%C3%A9matiques_de_l%27IH%C3%89S" title="Publications Mathématiques de l'IHÉS">Publications Mathématiques de l'IHÉS</a></i>. <b>32</b>: 5–361. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02732123">10.1007/bf02732123</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0238860">0238860</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+Math%C3%A9matiques+de+l%27IH%C3%89S&rft.atitle=%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%3A+IV.+%C3%89tude+locale+des+sch%C3%A9mas+et+des+morphismes+de+sch%C3%A9mas%2C+Quatri%C3%A8me+partie&rft.volume=32&rft.pages=5-361&rft.date=1967&rft_id=info%3Adoi%2F10.1007%2Fbf02732123&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0238860%23id-name%3DMR&rft.aulast=Grothendieck&rft.aufirst=Alexandre&rft.au=Dieudonn%C3%A9%2C+Jean&rft_id=http%3A%2F%2Fwww.numdam.org%2Farticles%2FPMIHES_1967__32__5_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i><a href="/wiki/Fondements_de_la_G%C3%A9ometrie_Alg%C3%A9brique" title="Fondements de la Géometrie Algébrique">Fondements de la Géometrie Algébrique</a></i> (<i>FGA</i>)</li> <li><i><a href="/wiki/S%C3%A9minaire_de_G%C3%A9om%C3%A9trie_Alg%C3%A9brique_du_Bois_Marie" title="Séminaire de Géométrie Algébrique du Bois Marie">Séminaire de Géométrie Algébrique du Bois Marie</a></i> (<i>SGA</i>)</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMumford2010" class="citation book cs1">Mumford, David (2010). <a href="/wiki/Ching-Li_Chai" title="Ching-Li Chai">Ching-Li Chai</a>; Amnon Neeman; Takahiro Shiota. (eds.). <i>Selected papers, Volume II. On algebraic geometry, including correspondence with Grothendieck</i>. Springer. pp. 720, 722. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-72491-1" title="Special:BookSources/978-0-387-72491-1"><bdi>978-0-387-72491-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Selected+papers%2C+Volume+II.+On+algebraic+geometry%2C+including+correspondence+with+Grothendieck.&rft.pages=720%2C+722&rft.pub=Springer&rft.date=2010&rft.isbn=978-0-387-72491-1&rft.aulast=Mumford&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLang,_S.1961" class="citation journal cs1"><a href="/wiki/Serge_Lang" title="Serge Lang">Lang, S.</a> (1961). <a rel="nofollow" class="external text" href="http://www.ams.org/journals/bull/1961-67-03/S0002-9904-1961-10564-8/S0002-9904-1961-10564-8.pdf">"Review: <i>Éléments de géométrie algébrique</i>, par A. Grothendieck, rédigés avec la collaboration de J. Dieudonné"</a> <span class="cs1-format">(PDF)</span>. <i>Bull. Amer. Math. Soc</i>. <b>67</b> (3): 239–246. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9904-1961-10564-8">10.1090/S0002-9904-1961-10564-8</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Review%3A+%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique%2C+par+A.+Grothendieck%2C+r%C3%A9dig%C3%A9s+avec+la+collaboration+de+J.+Dieudonn%C3%A9&rft.volume=67&rft.issue=3&rft.pages=239-246&rft.date=1961&rft_id=info%3Adoi%2F10.1090%2FS0002-9904-1961-10564-8&rft.au=Lang%2C+S.&rft_id=http%3A%2F%2Fwww.ams.org%2Fjournals%2Fbull%2F1961-67-03%2FS0002-9904-1961-10564-8%2FS0002-9904-1961-10564-8.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89l%C3%A9ments+de+g%C3%A9om%C3%A9trie+alg%C3%A9brique" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique&action=edit&section=6" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Scanned copies and partial English translations: <a rel="nofollow" class="external text" href="https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/pubtexts.php">Mathematical Texts (published)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20121104083946/http://www.math.jussieu.fr/~leila/grothendieckcircle/mathtexts.php">Archived</a> 2012-11-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li>Detailed table of contents: <a rel="nofollow" class="external text" href="http://perso.telecom-paristech.fr/~madore/ega-toc.pdf"><i>EGA</i></a></li> <li><a rel="nofollow" class="external text" href="https://agrothendieck.github.io"><i>SGA</i>, <i>EGA</i>, <i>FGA</i></a> by Mateo Carmona</li> <li><a rel="nofollow" class="external text" href="https://www.grothendieckcircle.org/">The Grothendieck circle</a> maintains copies of EGA, SGA, and other of Grothendieck's writings</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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