On de Rham--Witt Cohomology of Classifying Stacks

TL;DR

This paper constructs a specific example of a proper smooth fourfold over a field of characteristic p, exhibiting asymmetric Hodge--Witt numbers in degree 3, advancing understanding of cohomological properties in algebraic geometry.

Contribution

It provides the first explicit example of such asymmetry in Hodge--Witt numbers for a fourfold, using computations related to the classifying stack B alpha_p.

Findings

Example of a fourfold with asymmetric Hodge--Witt numbers in degree 3

Sharp in dimension and total degree

Uses computations of cohomology of classifying stacks

Abstract

We give an example of proper smooth fourfold over a perfect field k of characteristic p > 0 with asymmetric Hodge--Witt numbers in total degree 3. Our example is sharp both in terms of dimension and total degree. We arrive at our example by computing and approximating the Hodge--Witt cohomology groups of the classifying stack B alpha_p.