Semiampleness For Calabi-Yau Surfaces In Positive And Mixed Characteristic

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