Algebra & Number Theory

Higher direct images of the structure sheaf in positive characteristic

Andre Chatzistamatiou and Kay Rülling

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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.

Article information

Source
Algebra Number Theory, Volume 5, Number 6 (2011), 693-775.

Dates
Received: 2 December 2009
Revised: 17 January 2011
Accepted: 1 March 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729686

Digital Object Identifier
doi:10.2140/ant.2011.5.693

Mathematical Reviews number (MathSciNet)
MR2923726

Zentralblatt MATH identifier
1253.14013

Subjects
Primary: 14E05: Rational and birational maps
Secondary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]

Keywords
birational geometry rational singularities

Citation

Chatzistamatiou, Andre; Rülling, Kay. Higher direct images of the structure sheaf in positive characteristic. Algebra Number Theory 5 (2011), no. 6, 693--775. doi:10.2140/ant.2011.5.693. https://projecteuclid.org/euclid.ant/1513729686


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