![]() ![]() I'm only an "algebraic geometry enthusiast", so my advice should probably be taken with a grain of salt. It explains the general theory of algebraic groups, and the general representation theory of reductive groups using modern language: schemes, fppf descent, etc., in only 400 quatro-sized pages! That's enough to keep you at work for a few years!Ī brilliant epitome of SGA 3 and Gabriel-Demazure is Sancho de Salas, Grupos algebraicos y teoria de invariantes. You may amuse yourself by working out the first topics above over an arbitrary base. compactifications of the stack of abelian schemes (Faltings-Chai, Degeneration of abelian varieties Olsson, Canonical compactifications… Kato and Usui, Classidying spaces of degenerating polarized Hodge structures.).proof that abelian schemes assemble into an algebraic stack (Mumford, Geometric invariant theory, Chapter 7),.Lang-Néron theorem and $K/k$ traces (Brian Conrad's notes).questions of projectivity (Raynaud, Faisceaux amples sur les schemas…),.construction of the dual abelian scheme (Faltings-Chai, Degeneration of abelian varieties, Chapter 1),.the theorem of the cube (Raynaud, Faisceaux amples sur les schémas…),. ![]() ![]()
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