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.
Citation
Andre Chatzistamatiou. Kay Rülling. "Higher direct images of the structure sheaf in positive characteristic." Algebra Number Theory 5 (6) 693 - 775, 2011. https://doi.org/10.2140/ant.2011.5.693
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