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Higher direct images of the structure sheaf in positive characteristic

Andre Chatzistamatiou, Kay Rülling

Number 14
Authors Kay Rülling
Andre Chatzistamatiou
Year 2010

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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