Vanishing theorems for threefolds in characteristic $p>5$

TL;DR

This paper establishes vanishing theorems for threefold pairs in characteristic p>5, with applications to singularities and Mori fiber spaces, advancing the understanding of threefold geometry in positive characteristic.

Contribution

It proves Grauert-Riemenschneider-type vanishing theorems for threefold pairs in characteristic p>5, a significant extension in positive characteristic algebraic geometry.

Findings

Vanishing theorems hold for threefold pairs in characteristic p>5.

Applications include insights into dlt singularities.

Implications for Mori fiber spaces of threefolds.

Abstract

We prove Grauert-Riemenschneider-type vanishing theorems for excellent dlt threefolds pairs whose closed points have perfect residue fields of positive characteristic $p>5$. Then we discuss applications to dlt singularities and to Mori fiber spaces of threefolds.