A Grauert-Riemenschneider vanishing theorem for Witt canonical sheaves

TL;DR

This paper establishes a Witt vector analogue of the Grauert-Riemenschneider vanishing theorem in positive characteristic, leading to new insights into the rationality of certain singularities.

Contribution

It introduces a Witt vector version of the Grauert-Riemenschneider vanishing theorem, addressing a previously open question in algebraic geometry.

Findings

Proves a Witt vector version of the vanishing theorem in positive characteristic.

Derives rationality results for F-rational singularities.

Answers a question posed by previous researchers.

Abstract

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 R\"ulling. We then deduce some rationality consequences for $F$-rational singularities.