de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities

TL;DR

This paper proves the degeneration of the Hodge-de Rham spectral sequence for certain tame stacks and their coarse spaces in characteristic p, extending classical results to more general algebraic structures.

Contribution

It extends the degeneration results of the Hodge-de Rham spectral sequence to tame Artin stacks and their coarse spaces in characteristic p, including schemes with linearly reductive singularities.

Findings

Degeneration of the Hodge-de Rham spectral sequence for tame Artin stacks in characteristic p.

Extension of degeneracy results to schemes etale locally quotient of smooth schemes by linearly reductive groups.

Application to schemes with linearly reductive singularities in characteristic p.

Abstract

We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic p (as defined by Abramovich, Olsson, and Vistoli) which lift mod p^2 degenerates. We push the result to the coarse spaces of such stacks, thereby obtaining a degeneracy result for schemes which are etale locally the quotient of a smooth scheme by a finite linearly reductive group scheme.