Cohomology of classical algebraic groups from the functorial viewpoint.

DOI10.1016/j.aim.2010.02.014zbMath1208.20043arXiv0902.4459OpenAlexW2091575700MaRDI QIDQ986073

Antoine Touzé

Publication date: 11 August 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.4459

zbMATH Keywords

general linear groupsalgebraic groupscohomology groupssymplectic groupsHopf algebrasorthogonal groupsclassical groupsfunctorial representationsclassical invariant theorystrict polynomial functorsstable cohomology

Mathematics Subject Classification ID

Geometric invariant theory (14L24) Resolutions; derived functors (category-theoretic aspects) (18G10) Cohomology theory for linear algebraic groups (20G10) Linear algebraic groups over adèles and other rings and schemes (20G35) Functor categories, comma categories (18A25)

Related Items (11)

Graded analogues of one-parameter subgroups and applications to the cohomology of \(\mathrm{GL}_{m|n(r)}\) ⋮ A construction of the universal classes for algebraic groups with the twisting spectral sequence. ⋮ Quantum polynomial functors from \(e\)-Hecke pairs ⋮ Spin polynomial functors and representations of Schur superalgebras ⋮ Ringel duality and derivatives of non-additive functors ⋮ Sur la noethérianité locale des foncteurs polynomiaux ⋮ Cohomological finite-generation for finite supergroup schemes ⋮ Bar complexes and extensions of classical exponential functors ⋮ Connectedness of cup products for polynomial representations of \(\mathrm{GL}_n\) and applications ⋮ Computations and applications of some homological constants for polynomial representations of 𝐺𝐿_{𝑛} ⋮ Sur l'homologie des groupes unitaires à coefficients polynomiaux

Cites Work

• Cohomology of induced representations for algebraic groups
• Universal classes for algebraic groups.
• Bifunctor cohomology and cohomological finite generation for reductive groups.
• Rational and generic cohomology
• A characteristic free approach to invariant theory
• Cohomology of finite group schemes over a field
• General linear and functor cohomology over finite fields
• Sur quelques points d'algèbre homologique
• Exact categories
• On the adjoint quotient of Chevalley groups over arbitrary base schemes
• Extensions of strict polynomial functors
• Cohomology of bifunctors
• Sur l’homologie des groupes orthogonaux et symplectiques à coefficients tordus
• Higher algebraic K-theory: I
• Infinitesimal 1-parameter subgroups and cohomology
• Homology
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