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COHOMOLOGICAL INTEGRALITY FOR WEAKLY SYMMETRIC REPRESENTATIONS OF REDUCTIVE GROUPS

Part of: General commutative ring theory Algebraic groups

Published online by Cambridge University Press:  03 December 2025

Lucien Hennecart Open the ORCID record for Lucien Hennecart [Opens in a new window]
Lucien Hennecart*
Affiliation:
LAMFA, CNRS UMR 7352, CNRS Université de Picardie Jules Verne , Amiens, France
*
lucien.hennecart@u-picardie.fr
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Abstract

In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components indexed by some equivalence classes of cocharacters of a maximal torus. This decomposition enables the definition of new enumerative invariants associated with the stack, which we begin to explore.

Keywords

reductive groupscohomological integralityintersection cohomology

MSC classification

Primary: 14L30: Group actions on varieties or schemes (quotients) 14L24: Geometric invariant theory 13A50: Actions of groups on commutative rings; invariant theory

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , First View , pp. 1 - 37
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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