Semiampleness for Calabi--Yau surfaces in positive and mixed characteristic

TL;DR

This paper proves the semiampleness conjecture for Calabi--Yau surfaces over various base rings, confirming related conjectures and exploring implications for threefolds in mixed characteristic.

Contribution

It establishes the semiampleness conjecture for klt Calabi--Yau surfaces in positive and mixed characteristic, advancing understanding of abundance and related conjectures.

Findings

Semiampleness conjecture proven for Calabi--Yau surfaces

Generalized abundance and Serrano's conjecture confirmed for surfaces

Initial results on Calabi--Yau threefolds in mixed characteristic

Abstract

In this note we prove the semiampleness conjecture for klt Calabi--Yau surface pairs over an excellent base ring. As applications we deduce that generalised abundance and Serrano's conjecture hold for surfaces. Finally, we study the semiampleness conjecture for Calabi--Yau threefolds over a mixed characteristic DVR.