{"id":85,"date":"2016-06-23T21:58:28","date_gmt":"2016-06-23T19:58:28","guid":{"rendered":"http:\/\/berndt-schwerdtfeger.de\/?page_id=85"},"modified":"2026-01-22T18:36:07","modified_gmt":"2026-01-22T17:36:07","slug":"algebraic-geometry","status":"publish","type":"page","link":"https:\/\/berndt-schwerdtfeger.de\/?page_id=85","title":{"rendered":"Algebraic Geometry"},"content":{"rendered":"<h3><a name=\"vk\"><\/a>Introduction \u00e0 l&#8217;\u00e9tude des vari\u00e9t\u00e9s k\u00e4hl\u00e9riennes <small>par <em>Andr\u00e9 WEIL<\/em><\/small><\/h3>\n<ul>\n<li>version 1.0, 2015-01-29 : <a title=\"vk.pdf\" href=\"wp-content\/uploads\/pdf\/vk.pdf\"><img decoding=\"async\" src=\"wp-content\/uploads\/pdf.png\" alt=\"pdf\" \/><\/a><br \/>MSC Primary 32Q15, Secondary 11G10, 14K20, 14K25 <\/li>\n<\/ul>\n<p>L\u2019\u00e9dition en TeX du fascicule de Weil servira de le rendre disponible \u00e0 nouveau, les \u00e9ditions du livre \u00e9tant \u00e9puis\u00e9es depuis des ann\u00e9es.<\/p>\n<h3><a name=\"sga\"><\/a>S\u00e9minaire de g\u00e9om\u00e9trie alg\u00e9brique d&#8217;Orsay<br \/>\nAnn\u00e9e 1969\/70<br \/><small>en hommage \u00e0<br \/>\n<em>Michel DEMAZURE, Jean GIRAUD, Michel RAYNAUD et Jean-Louis VERDIER<\/em><\/small><\/h3>\n<p>R\u00e9\u00e9dition du s\u00e9minaire en TeX<\/p>\n<ul>\n<li>version 1.0, 2015-01-06 : <a title=\"sga.pdf\" href=\"wp-content\/uploads\/pdf\/sga.pdf\"><img decoding=\"async\" src=\"wp-content\/uploads\/pdf.png\" alt=\"pdf\" \/><\/a><br \/>first published: 2014-11-19<br \/>MSC Primary 14A10, Secondary 14B10, 14B20, 14B25 <\/li>\n<\/ul>\n<p>Un tirage provisoire des notes fut diffus\u00e9 pendant l&#8217;ann\u00e9e scolaire, pour longtemps \u00e9tant rest\u00e9 in\u00e9dites. Enfin, une num\u00e9risation  de ces notes est apparu en ligne \u00e0 la <a title=\"Biblioth\u00e8que math\u00e9matique d'Orsay\" href=\"https:\/\/bibliotheque.math.u-psud.fr\/\" target=\"_blank\" rel=\"noopener noreferrer\">biblioth\u00e8que math\u00e9matique d&#8217;Orsay<\/a> (Jacques Hadamard), malheureusement d&#8217;une qualit\u00e9 d\u00e9plorable. Une r\u00e9daction d&#8217;ensemble et transcription en TeX me semblait souhaitable.<\/p>\n<h3><a name=\"theta\"><\/a>On theta functions<\/h3>\n<ul>\n<li>version 1.0 (restored) 2007-10-07 : <a title=\"theta.pdf\" href=\"wp-content\/uploads\/pdf\/theta.pdf\"><img decoding=\"async\" src=\"wp-content\/uploads\/\/pdf.png\" alt=\"pdf\" \/><\/a><br \/>first published: 2007-10-07<br \/>MSC Primary 14H42, Secondary 14K25 <\/li>\n<\/ul>\n<p>In this paper I present the foundation of Jacobi&#8217;s \u03d1-functions, based on his 1838 lecture on the same subject. I derive all his \u03d1-relations, in particular his <em>merkw\u00fcrdige Relation [Jacobi]<\/em> of <em>theta-constants<\/em> <br \/> \u03d1(0,\u03c4)<sup>4<\/sup> = \u03d1<sub>01<\/sub>(0,\u03c4)<sup>4<\/sup> + \u03d1<sub>10<\/sub>(0,\u03c4)<sup>4<\/sup> <br \/> which relates to my paper on the <a title=\"\u03b6-function\" href=\"https:\/\/berndt-schwerdtfeger.de\/?page_id=87#v4\">\u03b6-function<\/a> of the curve <em>C : x<sup>4<\/sup> + y<sup>4<\/sup> + z<sup>4<\/sup> = 0<\/em>.  A subsequent paper on <em>modular curves<\/em> will give more detail.<\/p>\n<h3><a name=\"gfet\"><\/a>Groupe fondamental \u00e9tale et topologique <small>par <em>Jean-Louis VERDIER<\/em><\/small><\/h3>\n<ul>\n<li>version 1.2, 2015-01-21 : <a title=\"gfet.pdf\" href=\"wp-content\/uploads\/pdf\/gfet.pdf\"><img decoding=\"async\" src=\"wp-content\/uploads\/\/pdf.png\" alt=\"pdf\" \/><\/a><br \/>first published: 2007-09-28<br \/>MSC Primary 14H30 <\/li>\n<\/ul>\n<p>Ce texte s&#8217;oriente d&#8217;un cours profess\u00e9 par Jean-Louis Verdier \u00e0 la facult\u00e9 des sciences d&#8217;Orsay pendant les mois f\u00e9vrier &#8211; avril 1970, dont j&#8217;\u00e9tais l&#8217;auditeur. J&#8217;ai transcrit les notes du cours en TeX pour obtenir une r\u00e9f\u00e9rence facilement accessible.<br \/>Jean-Louis Verdier, n\u00e9 2 f\u00e9vrier 1935, est disparu en 28 ao\u00fbt 1989.<\/p>\n<p>En la nouvelle version 1.2 j&#8217;ai mis \u00e0 jour les r\u00e9f\u00e9rences, en particulier ajout\u00e9 une citation du s\u00e9minaire SGA d&#8217;Orsay de 1969-70.<\/p>\n<h3><a name=\"riem\"><\/a>Surfaces de Riemann compactes <small>par <em>Jean GIRAUD<\/em><\/small><\/h3>\n<ul>\n<li><img decoding=\"async\" src=\"wp-content\/uploads\/new.gif\" alt=\"new\" \/> version 1.4, 2026-01-22 : <a title=\"riemann.pdf\" href=\"wp-content\/uploads\/pdf\/riemann.pdf\"><img decoding=\"async\" src=\"wp-content\/uploads\/\/pdf.png\" alt=\"pdf\" \/><\/a><br \/>first published: 2005-06-28<br \/> MSC Primary 30F10, Secondary 14H05, 14H55 <\/li>\n<\/ul>\n<p>Ce texte rassemble les notes d&#8217;un cours profess\u00e9 par Jean Giraud \u00e0 Orsay au second semestre de l&#8217;ann\u00e9e scolaire 1969-70 dans le cadre du troisi\u00e8me cycle de G\u00e9om\u00e9trie Alg\u00e9brique.<\/p>\n<p>Je lui remercie pour m&#8217;avoir permis de publier ces notes du cours. Il va de soi que toutes les fautes de frappe qui restent dans le texte ne lui sont d\u00fb.<br \/>Jean Giraud est disparu en 28 mars 2007.<\/p>\n<p>Dans cette \u00e9dition v1.4 j\u2019ai ajout\u00e9 l\u2019\u00e9nonc\u00e9 et la preuve du th\u00e9or\u00e8me de Riemann\u2013Roch pour un module coh\u00e9rent quelconque, ce que Giraud recommandait au lecteur \u00e0 titre d\u2019exercise dans l\u2019introduction.<\/p>\n<h3>Guide to l-adic cohomology<\/h3>\n<ul>\n<li>version 1.1, 2002-07-10 : <a title=\"lac.pdf\" href=\"wp-content\/uploads\/pdf\/lac.pdf\"><img decoding=\"async\" src=\"wp-content\/uploads\/pdf.png\" alt=\"pdf\" \/><\/a><br \/>first published: 2002-04-25<br \/>MSC Primary 14F20, Secondary 20C11 <\/li>\n<\/ul>\n<p>This guide (Leitfaden) was presented in the winter term 1977\/78 in the seminar of Claus Michael Ringel at University of Bonn. Its purpose is to break a path thru the jungle of SGA 4-5, to gather the most important definitions and theorems of l-adic cohomology. For the proofs exact signposts into SGA are given.<\/p>\n<h3>Topology, Sheaves and Flat Descent<\/h3>\n<ul>\n<li>version 1.0, 2012-11-10 : <a title=\"flat.pdf\" href=\"wp-content\/uploads\/pdf\/flat.pdf\"><img decoding=\"async\" src=\"wp-content\/uploads\/pdf.png\" alt=\"pdf\" \/><\/a><br \/>first published: 1999-08-08<br \/> MSC Primary 18F10, Secondary 14F20 <\/li>\n<\/ul>\n<p>This is a series of talks on Sheaves and Topology that I have given in the Seminar on Algebraic Geometry in Summer 1978 at the Faculty of Mathematics of the University of Bielefeld.<\/p>\n<p>Its main purpose is a fast introduction to flat descent theory. The audience is expected to have some familiarity with schemes. Full references are given where necessary.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction \u00e0 l&#8217;\u00e9tude des vari\u00e9t\u00e9s k\u00e4hl\u00e9riennes par Andr\u00e9 WEIL version 1.0, 2015-01-29 : MSC Primary 32Q15, Secondary 11G10, 14K20, 14K25 L\u2019\u00e9dition en TeX du fascicule de Weil servira de le rendre disponible \u00e0 nouveau, les \u00e9ditions du livre \u00e9tant \u00e9puis\u00e9es depuis des ann\u00e9es. S\u00e9minaire de g\u00e9om\u00e9trie alg\u00e9brique d&#8217;Orsay Ann\u00e9e 1969\/70en hommage \u00e0 Michel DEMAZURE, Jean [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":57,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ngg_post_thumbnail":0,"footnotes":""},"class_list":["post-85","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/pages\/85","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=85"}],"version-history":[{"count":39,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/pages\/85\/revisions"}],"predecessor-version":[{"id":1052,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/pages\/85\/revisions\/1052"}],"up":[{"embeddable":true,"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=\/wp\/v2\/pages\/57"}],"wp:attachment":[{"href":"https:\/\/berndt-schwerdtfeger.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=85"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}