References to SGA 8 and descent theory - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T04:28:19Z http://mathoverflow.net/feeds/question/85134 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/85134/references-to-sga-8-and-descent-theory References to SGA 8 and descent theory rghthndsd 2012-01-07T16:13:43Z 2012-01-08T12:11:35Z <p>In Geometric Invariant Theory, by Mumford, Fogarty, and Kirwan, if there is a mention of descent theory, it almost always comes along with a reference to SGA 8, Theorem 5.2 (see the end of the proof of prop 6.9 on page 119, for example). Now I know SGA 8 was never made, but I was wondering:</p> <ol> <li><p>Does anyone have a good guess as to what this theorem should say?</p></li> <li><p>Does anyone have a good reference for a quick and "hands off" introduction to descent theory? I am really just looking to understand the "gist" of it.</p></li> </ol> http://mathoverflow.net/questions/85134/references-to-sga-8-and-descent-theory/85185#85185 Answer by a-fortiori for References to SGA 8 and descent theory a-fortiori 2012-01-08T12:11:35Z 2012-01-08T12:11:35Z <p>For question 1, see the comment above.</p> <p>Collecting the answers to question 2:</p> <ul> <li>Grothendieck's original <em>FGA</em>, starting with <a href="http://www.numdam.org/numdam-bin/fitem?id=SB_1958-1960__5__299_0" rel="nofollow">TDTE I</a></li> <li>Vistoli's chapter in <em>FGA explained</em>, for the connection with stacks</li> <li><a href="http://mathoverflow.net/questions/22032/what-is-descent-theory" rel="nofollow">http://mathoverflow.net/questions/22032/what-is-descent-theory</a> for a very short overview</li> <li>Bosch-Lütkebohmert-Raynaud, <em>Néron Models</em> (recommended by BCnrd in the above-mentioned thread)</li> <li>Waterhouse, <em>Introduction to Affine Group Schemes</em>, containing a 20-page introduction primarily concerned with the affine case</li> </ul> <p>"Community wiki" post, feel free to modify.</p>