Duke Mathematical Journal

Bifunctor cohomology and cohomological finite generation for reductive groups

Antoine Touzé and Wilberd Van Der Kallen

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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 states 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 in [22]. We also continue the study of bifunctor cohomology of $\Gamma^*(\mathfrak{gl}^{(1)})$

Article information

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

Dates
First available in Project Euclid: 14 January 2010

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1263478512

Digital Object Identifier
doi:10.1215/00127094-2009-065

Mathematical Reviews number (MathSciNet)
MR2598378

Zentralblatt MATH identifier
1196.20053

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

Citation

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. http://projecteuclid.org/euclid.dmj/1263478512.


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