On de Rham--Witt Cohomology of Classifying Stacks

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.