Hodgetode Rham degeneration for stacks
Abstract
We introduce a notion of a Hodgeproper stack and extend the method of DeligneIllusie to prove the Hodgetode Rham degeneration in this setting. In order to reduce the statement in characteristic $0$ to characteristic $p$, we need to find a good integral model of a stack (a socalled spreading), which, unlike in the case of schemes, need not to exist in general. To address this problem we investigate the property of spreadability in more detail by generalizing standard spreading out results for schemes to higher Artin stacks and showing that all proper and some global quotient stacks are Hodgeproperly spreadable. As a corollary we deduce a (noncanonical) Hodge decomposition of the equivariant cohomology for certain classes of varieties with an algebraic group action.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.12665
 Bibcode:
 2019arXiv191012665K
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 Mathematics  Representation Theory
 EPrint:
 27 pages