Bifunctor cohomology and Cohomological finite generation for reductive groups

Details Bifunctor cohomology and Cohomological finite generation for reductive groups Bifunctor cohomology and Cohomological finite generation for reductive groups

2008-09-05

arxiv.org/abs/0809.1014v3

Duke Mathematical Journal. Vol. 151, No. 2, 2010, pp. 251-278.

Mathematics

Representation Theory

30 pages. v2. Part I reorganized and shortened, presentation of some proofs improved. To appear in Duke Math. J

Scientific paper

10.1215/00127094-2009-065

Let G be a reductive linear algebraic group over a field k. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory tells that the ring of invariants A^G=H^0(G,A) is finitely generated. We show that in fact the full cohomology ring H^*(G,A) is finitely generated. The proof is based on the strict polynomial bifunctor cohomology classes constructed by the junior author. We also continue the study of bifunctor cohomology of the divided powers of a Frobenius twist of the adjoint representation.

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