摘要 : We prove vanishing of the higher direct images of the structure (and the canon-ical) 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 ... 展开 We prove vanishing of the higher direct images of the structure (and the canon-ical) 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 vari-eties the cohomology of the structure sheaf is a birational invariant. These results are well known in characteristic zero. 收起