Duke Mathematical Journal

Bifunctor cohomology and cohomological finite generation for reductive groups

Antoine Touzé and Wilberd Van Der Kallen

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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))

Article information

Duke Math. J. Volume 151, Number 2 (2010), 251-278.

First available in Project Euclid: 14 January 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20G10: Cohomology theory
Secondary: 14L24: Geometric invariant theory [See also 13A50]


Touzé, Antoine; Van Der Kallen, Wilberd. Bifunctor cohomology and cohomological finite generation for reductive groups. Duke Math. J. 151 (2010), no. 2, 251--278. doi:10.1215/00127094-2009-065. https://projecteuclid.org/euclid.dmj/1263478512

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