English

Universal classes for algebraic groups

Representation Theory 2019-12-19 v2

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.

Keywords

Cite

@article{arxiv.0809.0989,
  title  = {Universal classes for algebraic groups},
  author = {Antoine Touzé},
  journal= {arXiv preprint arXiv:0809.0989},
  year   = {2019}
}

Comments

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

R2 v1 2026-06-21T11:17:15.114Z