Geodesic
Hodge-Witt cohomology and Witt-rational singularities
Documenta mathematica, Tome 17 (2012), pp. 663-781.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14J17, 14C25, 14F30
Keywords: de Rham-Witt complex, ekedahl duality, correspondences, singularities, Witt-vector cohomology 
@article{DOCMA_2012__17__a8,
     author = {Chatzistamatiou, Andre and R\"ulling, Kay},
     title = {Hodge-Witt cohomology and {Witt-rational} singularities},
     journal = {Documenta mathematica},
     pages = {663--781},
     publisher = {mathdoc},
     volume = {17},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a8/}
}
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Chatzistamatiou, Andre; Rülling, Kay. Hodge-Witt cohomology and Witt-rational singularities. Documenta mathematica, Tome 17 (2012), pp. 663-781. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a8/