Duke Mathematical Journal

Hodge theory of classifying stacks

Burt Totaro

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We compute the Hodge and the de Rham cohomology of the classifying space BG (defined as étale 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.

Article information

Duke Math. J., Volume 167, Number 8 (2018), 1573-1621.

Received: 29 January 2017
Revised: 9 January 2018
First available in Project Euclid: 22 March 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10]
Secondary: 20G05: Representation theory 57T10: Homology and cohomology of Lie groups

Hodge cohomology de Rham cohomology classifying space algebraic stack reductive group representation theory torsion prime


Totaro, Burt. Hodge theory of classifying stacks. Duke Math. J. 167 (2018), no. 8, 1573--1621. doi:10.1215/00127094-2018-0003. https://projecteuclid.org/euclid.dmj/1521684060

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