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