Mori fibre spaces for $3$-folds over imperfect fields

TL;DR

This paper extends the minimal model program to threefolds over function fields in characteristic p>5, establishing new results on the behavior of the canonical divisor and log canonical thresholds.

Contribution

It proves the LMMP for threefolds over imperfect fields with non-pseudo-effective canonical divisors and confirms ACC for log canonical thresholds in this setting.

Findings

LMMP holds for threefolds over function fields in characteristic p>5

ACC for log canonical thresholds established in this context

Advances understanding of minimal model program in positive characteristic

Abstract

We prove that the LMMP works for projective threefolds over function fields of characteristic $p>5$ when the canonical divisor is not pseudo-effective. In the process we show that ACC for log canonical thresholds holds in complete generality for threefolds in residue characteristic $p>5$.