Higher direct images of the structure sheaf in positive characteristic

Chatzistamatiou, Andre; Rülling, Kay

doi:10.2140/ant.2011.5.693

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Higher direct images of the structure sheaf in positive characteristic

Andre Chatzistamatiou and Kay Rülling

Vol. 5 (2011), No. 6, 693–775

DOI: 10.2140/ant.2011.5.693

Abstract

We prove vanishing of the higher direct images of the structure (and the canonical) sheaf for a proper birational morphism with source a smooth variety and target the quotient of a smooth variety by a finite group of order prime to the characteristic of the ground field. We also show that for smooth projective varieties the cohomology of the structure sheaf is a birational invariant. These results are well known in characteristic zero.

Keywords

birational geometry, rational singularities

Mathematical Subject Classification 2000

Primary: 14E05

Secondary: 14C17

Milestones

Received: 2 December 2009

Revised: 17 January 2011

Accepted: 1 March 2011

Published: 2 April 2012

Authors

Andre Chatzistamatiou
Fachbereich Mathematik, Campus Essen University of Duisburg-Essen D-45117 Essen Germany

Kay Rülling
Fachbereich Mathematik, Campus Essen University of Duisburg-Essen D-45117 Essen Germany

Vol. 5, No. 6, 2011