A Witt Nadel vanishing theorem for threefolds

TL;DR

This paper proves a Witt Nadel vanishing theorem for threefolds over fields of characteristic >5, with applications to divisibility of rational points on certain algebraic varieties.

Contribution

It introduces a new vanishing theorem for Witt multiplier ideals on threefolds in positive characteristic, extending previous results to a broader class of varieties.

Findings

Vanishing theorem for Witt multiplier ideals on threefolds

Divisibility of rational points on non-klt threefolds with anti-ample canonical divisor

Application to algebraic geometry over finite fields

Abstract

In this paper, we establish a vanishing theorem of Nadel type for the Witt multiplier ideals on threefolds over perfect fields of characteristic larger than five. As an application, if a projective normal threefold over $\mathbb{F}_q$ is not klt and its canonical divisor is anti-ample, then the number of the rational points on the klt-locus is divisible by $q$.