Hodge theory of classifying stacks

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.

38 pages; v2: title changed, definition improved, description of equivariant Hodge cohomology added

References in corpus (2)

• Integral p-adic Hodge theory
• Completions and derived de Rham cohomology

Cited by in corpus (7)

• Cohomology of the moduli stack of algebraic vector bundles
• Dieudonné Theory via Cohomology of Classifying Stacks
• Computations of de Rham cohomology rings of classifying stacks at torsion primes
• Rigid-analytic varieties with projective reduction violating Hodge symmetry
• Moduli of $\ell$-adic pro-étale local systems for smooth non-proper schemes
• Motivic cohomology and infinitesimal group schemes
• Steenrod operations on the de Rham cohomology of algebraic stacks