English

Hodge theory of classifying stacks

Algebraic Geometry 2018-07-18 v2 Representation Theory

Abstract

We compute the Hodge and de Rham cohomology of the classifying space BG (defined as etale cohomology on the algebraic stack BG) for reductive groups G over many fields, including fields of small characteristic. These calculations have a direct relation with representation theory, yielding new results there. The calculations are closely analogous to, but not always the same as, the cohomology of classifying spaces in topology.

Keywords

Cite

@article{arxiv.1703.03545,
  title  = {Hodge theory of classifying stacks},
  author = {Burt Totaro},
  journal= {arXiv preprint arXiv:1703.03545},
  year   = {2018}
}

Comments

38 pages; v2: title changed, definition improved, description of equivariant Hodge cohomology added

R2 v1 2026-06-22T18:41:56.521Z