Hodge-Witt Cohomology and Witt-Rational Singularities

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.

2010 Mathematics Subject Classification: 14J17, 14C25, 14F30

Keywords and Phrases: De Rham-Witt complex, Ekedahl duality, correspondences, singularities, Witt-vector cohomology

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