Duke Mathematical Journal

Hodge theory of classifying stacks

Burt Totaro

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1521684060

Digital Object Identifier
doi:10.1215/00127094-2018-0003

Mathematical Reviews number (MathSciNet)
MR3807317

Zentralblatt MATH identifier
06896953

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

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

Citation

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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