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Duke University Press, Duke Mathematical Journal, 2(151), 2010

DOI: 10.1215/00127094-2009-065

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Bifunctor cohomology and cohomological finite generation for reductive groups

Journal article published in 2010 by Antoine Touze, Wilberd Van Der Kallen
This paper is available in a repository.
This paper is available in a repository.

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Abstract

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