On the termination of the MMP for semi-stable fourfolds in mixed characteristic

TL;DR

This paper advances the understanding of the minimal model program (MMP) by proving its termination for semi-stable fourfolds in mixed characteristic under new conditions, especially over Dedekind schemes with perfect residue fields of characteristic greater than 5.

Contribution

It extends the termination results of the MMP to broader classes of semi-stable fourfolds in mixed characteristic, improving upon previous work by Hacon and Witaszek.

Findings

MMP terminates for semi-stable fourfolds over Dedekind schemes with perfect residue fields

Validates MMP for strictly semi-stable fourfolds in mixed characteristic

Results hold when residue field characteristics are greater than 5

Abstract

We improve on the result of Hacon and Witaszek by showing that the MMP for semi-stable fourfolds in mixed characteristic terminates in several new situations. In particular, we show the validity of the MMP for strictly semi-stable fourfolds over excellent Dedekind schemes globally when the residue fields are perfect and have characteristics $p>5$.