Abstract
We compute the Hodge and the de Rham cohomology of the classifying space (defined as étale cohomology on the algebraic stack ) for reductive groups 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.
Citation
Burt Totaro. "Hodge theory of classifying stacks." Duke Math. J. 167 (8) 1573 - 1621, 1 June 2018. https://doi.org/10.1215/00127094-2018-0003
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