Description:

Title: A Grauert-Riemenschneider vanishing theorem for Witt canonical sheaves

Abstract: A useful vanishing theorem for understanding characteristic zero singularities is Grauert-Riemenschneider vanishing, which asserts that if f: Y -> X is a projective birational morphism and Y is smooth, then higher pushfowards of \omega_Y vanish. A remarkable consequence of this result is that characteristic zero klt singularities are rational. As one could expect, this vanishing theorem fails in positive characteristic. In this talk, we will explain how to prove a Witt vector version of Grauert-Riemenchneider vanishing, answering a question of Blickle, Esnault, Chatzistamatiaou and Rülling. We will also discuss applications to singularities.