Vol. 5, No. 6, 2011

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Higher direct images of the structure sheaf in positive characteristic

Andre Chatzistamatiou and Kay Rülling

Vol. 5 (2011), No. 6, 693–775
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