Quasi-$F$-splitting and smooth weak del Pezzo surfaces in mixed characteristic

Abstract

We introduce the notion of quasi-$F$-splitting in mixed characteristic and study Kodaira-type vanishing on quasi-$F$-splitting varieties. As an application, we prove a Kodaira-type vanishing on lifts of rational double point (RDP) del Pezzo surfaces.

17 pages. The title has changed, the previous title is "Quasi-$F$-splitting of smooth weak del Pezzo in mixed characteristic"