Semiampleness for Calabi--Yau surfaces in positive and 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.

26 pages, v2: minor revisions. To appear in Nagoya Math. J