Higher direct images of the structure sheaf in positive characteristic (Q435258)

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 \(0\).