## Hodge-Witt cohomology and Witt-rational singularities

### Summary

Summary: We prove the vanishing modulo torsion of the higher direct images of the sheaf of Witt vectors (and the Witt canonical sheaf) for a purely inseparable projective alteration between normal finite quotients over a perfect field. For this, we show that the relative Hodge-Witt cohomology admits an action of correspondences. As an application we define Witt-rational singularities which form a broader class than rational singularities. In particular, finite quotients have Witt-rational singularities. In addition, we prove that the torsion part of the Witt vector cohomology of a smooth, proper scheme is a birational invariant.

### Mathematics Subject Classification

14J17, 14C25, 14F30

### Keywords/Phrases

de Rham-Witt complex, ekedahl duality, correspondences, singularities, Witt-vector cohomology