A vanishing theorem for threefolds in characteristic $p>5$ and applications

Abstract

In this note we show a Kawamata-Viehweg vanishing theorem for pl-contractions on threefolds in characteristic $p>5$. We deduce several applications for klt threefolds: the vanishing of higher direct images of structure sheaves of Mori fibre spaces, Koll\'ar's result on local vanishing and the rationality of the singularities of the base of a conic bundle.