A Grauert–Riemenschneider vanishing theorem for Witt canonical sheaves

Abstract We prove a Witt vector version of the usual Grauert–Riemenschneider vanishing theorem over perfect fields of positive characteristic, solving a question raised by Blickle, Esnault, Chatzistamatiou and Rülling. We then deduce some rationality consequences for $F$ F –rational singularities.