Abundance theorem for threefolds in mixed characteristic

TL;DR

This paper proves the abundance theorem for certain threefold pairs in mixed characteristic and provides conditions for the invariance of plurigenera in families of singular surfaces.

Contribution

It establishes the abundance theorem for arithmetic klt threefolds in mixed characteristic and links it to invariance of plurigenera in specific surface families.

Findings

Proves abundance theorem for threefolds in mixed characteristic

Provides conditions for invariance of plurigenera

Connects threefold results to surface family invariance

Abstract

We show the abundance theorem for arithmetic klt threefold pairs whose closed point have residue characteristic greater than five. As a consequence, we give a sufficient condition for the asymptotic invariance of plurigenera for certain families of singular surface pairs to hold in mixed characteristic.