1 February 2010 Bifunctor cohomology and cohomological finite generation for reductive groups
Antoine Touzé, Wilberd Van Der Kallen
Author Affiliations +
Duke Math. J. 151(2): 251-278 (1 February 2010). DOI: 10.1215/00127094-2009-065

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 states that the ring of invariants AG=H0(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 in [22]. We also continue the study of bifunctor cohomology of Γ*(gl(1))

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Antoine Touzé. Wilberd Van Der Kallen. "Bifunctor cohomology and cohomological finite generation for reductive groups." Duke Math. J. 151 (2) 251 - 278, 1 February 2010. https://doi.org/10.1215/00127094-2009-065

Information

Published: 1 February 2010
First available in Project Euclid: 14 January 2010

zbMATH: 1196.20053
MathSciNet: MR2598378
Digital Object Identifier: 10.1215/00127094-2009-065

Subjects:
Primary: 20G10
Secondary: 14L24

Rights: Copyright © 2010 Duke University Press

Vol.151 • No. 2 • 1 February 2010
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