# Higher direct images of the structure sheaf in positive characteristic

Andre Chatzistamatiou, Kay Rülling

Number | 14 |
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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.