On the existence of flips for threefolds in mixed characteristic $(0,5)$

TL;DR

This paper proves the validity of the Minimal Model Program for threefolds over certain schemes in mixed characteristic, specifically excluding residue fields of characteristic 2 or 3, advancing the understanding of algebraic geometry in mixed characteristic settings.

Contribution

It provides a detailed proof of the Minimal Model Program for threefolds in mixed characteristic (0,5), extending previous results to new settings.

Findings

Validates the Minimal Model Program for threefolds in mixed characteristic (0,5)

Excludes residue fields of characteristic 2 or 3

Enhances understanding of algebraic geometry in mixed characteristic contexts

Abstract

We provide a detailed proof of the validity of the Minimal Model Program for threefolds over excellent Dedekind separated schemes whose residue fields do not have characteristic 2 or 3.