Bifunctor Cohomology and Cohomological Finite Generation for Reductive Groups
نویسندگان
چکیده
LetG be a reductive linear algebraic group over a field k. LetA be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory states that the ring of invariantsA = H 0(G,A) is finitely generated. We show that in fact the full cohomology ringH ∗(G,A) is finitely generated. The proof is based on the strict polynomial bifunctor cohomology classes constructed in [22]. We also continue the study of bifunctor cohomology of ∗(gl(1)).
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تاریخ انتشار 2008