Higher direct images of the structure sheaf in positive characteristic

By A. Chatzistamatiou, Kay Rulling. 2009

84 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/17c2e37abe4b2ccca5b96c4975a49de2531209a6