A Grauert-Riemenschneider vanishing theorem for Witt canonical sheaves

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