Higher direct images of the structure sheaf in positive characteristic
In the article under review, the authors prove that for smooth projective varieties, the cohomology of the structure sheaf is a birational invariant and they show the vanishing of higher direct images of the structure and canonical sheaves for a proper birational morphism from a smooth variety to the quotient of a smooth variety by a finite group of order prime to the characteristic of the ground field. These results are well known in characteristic \(0\).
scientific article; zbMATH DE number 6054518