Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic

TL;DR

This paper advances the minimal model program for three-dimensional algebraic varieties in mixed characteristic, extending global regularity concepts and Fujita's conjecture to new settings.

Contribution

It generalizes global F-regularity to mixed characteristic and applies it to establish the minimal model program for threefolds with residue characteristics over five.

Findings

Established the MMP for arithmetic threefolds in mixed characteristic

Generalized global F-regularity to mixed characteristic

Extended Fujita's conjecture to mixed characteristic cases

Abstract

We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global $F$-regularity to mixed characteristic and identify certain stable sections of adjoint line bundles. Finally, by passing to graded rings, we generalize a special case of Fujita's conjecture to mixed characteristic.