Geodesic
Hodge-Witt cohomology and Witt-rational singularities
Documenta mathematica, Tome 17 (2012), pp. 663-781
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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.
DOI : 10.4171/dm/380
Classification : 14C25, 14F30, 14J17
Mots-clés : singularities, de Rham-Witt complex, ekedahl duality, correspondences, Witt-vector cohomology 
@article{10_4171_dm_380,
     author = {Andre Chatzistamatiou and Kay R\"ulling},
     title = {Hodge-Witt cohomology and {Witt-rational} singularities},
     journal = {Documenta mathematica},
     pages = {663--781},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/380},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/380/}
}
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Andre Chatzistamatiou; Kay Rülling. Hodge-Witt cohomology and Witt-rational singularities. Documenta mathematica, Tome 17 (2012), pp. 663-781. doi: 10.4171/dm/380

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