Universal classes for algebraic groups

Abstract

We exhibit cocycles representing certain classes in the rational cohomology of of the general linear group with coefficients in the divided powers of a Frobenius twist of the adjoint representation. These classes' existence was anticipated by van der Kallen, and they intervene in the proof that reductive linear algebraic groups have finitely generated cohomology algebras.

24 pages. v2, slight modifications : corollary 0.2 added, additional comments in section 2, one reference added. To appear in Duke Math. J

References in corpus (3)

• Bifunctor cohomology and Cohomological finite generation for reductive groups
• Cohomology of bifunctors
• Finite Schur filtration dimension for modules over an algebra with Schur filtration

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• Cohomological finite generation for the group scheme $S{L}_2$
• Sur la noeth{é}rianit{é} locale des foncteurs polynomiaux
• Ext-groups in the Category of Strict Polynomial Functors