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arXiv · 1703.03545

Hodge theory of classifying stacks

Burt Totaro
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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.

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Burt Totaro. 2017-03-10. Hodge theory of classifying stacks. https://doi.org/10.1215/00127094-2018-0003

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