Bifunctor cohomology and cohomological finite generation for reductive groups.

DOI10.1215/00127094-2009-065zbMath1196.20053arXiv0809.1014OpenAlexW3098279298MaRDI QIDQ849199

Antoine Touzé, Wilberd van der Kallen

Publication date: 25 February 2010

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.1014

zbMATH Keywords

cohomology ringsreductive groupsdivided powersrational cohomologycohomological finite generationcohomology of general linear groupsbifunctor cohomologystrict polynomial bifunctorsuniversal cohomology classes

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Resolutions; derived functors (category-theoretic aspects) (18G10) Cohomology theory for linear algebraic groups (20G10)

Related Items (12)

Finite generation of cohomology for Drinfeld doubles of finite group schemes ⋮ A construction of the universal classes for algebraic groups with the twisting spectral sequence. ⋮ Universal classes for algebraic groups. ⋮ Superized Troesch complexes and cohomology for strict polynomial superfunctors ⋮ The ring of polynomial functors of prime degree ⋮ Ringel duality and derivatives of non-additive functors ⋮ Additive polynomial superfunctors and cohomology ⋮ Sur la noethérianité locale des foncteurs polynomiaux ⋮ Finite generation properties of cohomology rings for infinite groups. ⋮ Cohomological finite generation for the group scheme \(SL2\) ⋮ Cohomology of classical algebraic groups from the functorial viewpoint. ⋮ The mathematics of Andrei Suslin

Cites Work

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• Finite Schur filtration dimension for modules over an algebra with Schur filtration.
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• Geometrically reductive Hopf algebras
• Rational and generic cohomology
• Invariant theory
• Geometrically reductive affine group schemes
• Cohomology of finite group schemes over a field
• Algebraic homogeneous spaces and invariant theory
• Invariants of a group in an affine ring
• Products in exact couples
• The Cohomology Ring of a Finite Group
• Cohomology of bifunctors
• Filtrations of $G$-modules
• Infinitesimal 1-parameter subgroups and cohomology

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