Existence of Mori fibre spaces for 3-folds in char $p$

TL;DR

This paper establishes fundamental results in the minimal model program for three-dimensional algebraic varieties over fields of characteristic greater than 5, including the existence of Mori fibre spaces.

Contribution

It proves key theorems such as the cone, base point free, contraction theorems, and the existence of Mori fibre spaces for 3-folds in characteristic p > 5, extending the minimal model program.

Findings

Proved the cone theorem for 3-folds in char p>5

Established the existence of Mori fibre spaces in this setting

Confirmed finiteness of minimal models and termination with scaling

Abstract

We prove the following results for projective klt pairs of dimension $3$ over an algebraically closed field of char $p>5$: the cone theorem, the base point free theorem, the contraction theorem, finiteness of minimal models, termination with scaling, existence of Mori fibre spaces, etc.