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Hodge-Witt cohomology and Witt-rational singularities

By Andre Chatzistamatiou and Kay Rülling

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.Comment: 105 page

Topics: Mathematics - Algebraic Geometry
Year: 2011
OAI identifier: oai:arXiv.org:1104.2145
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