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arXiv · 1104.2145

Hodge-Witt cohomology and Witt-rational singularities

Andre Chatzistamatiou·Kay Rülling
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Abstract

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.

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Andre Chatzistamatiou, Kay Rülling. 2011-04-12. Hodge-Witt cohomology and Witt-rational singularities. https://arxiv.org/abs/1104.2145

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