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arXiv · 0911.3599

Higher direct images of the structure sheaf in positive characteristic

Andre Chatzistamatiou·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.

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Andre Chatzistamatiou, Kay Rülling. 2011-04-13. Higher direct images of the structure sheaf in positive characteristic. https://arxiv.org/abs/0911.3599

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