Birational invariance of relative Witt vector cohomology

Abstract   In the talk we report on work in progress joint with Andre Chatzistamatiou. Let S be an algebraic scheme  over a perfect field k of positive characteristic, then we explain why relative Witt vector cohomology of an S -scheme which is smooth and projective over k, is a birational invariant of X/S. We will also consider the case of quotient singularities and give applications to the study of (Witt-) rational singularities and congruences for the number of rational points in a finite field.