Klt del Pezzo surfaces which are not globally F-split

We construct a klt del Pezzo surface which is not globally F-split, over any algebraically closed field of positive characteristic.Comment: 18 page

On log del Pezzo surfaces in large characteristic

We show that any Kawamata log terminal del Pezzo surface over an algebraically closed field of large characteristic is globally F-regular or it admits a log resolution which is liftable to characteristic zero. As a consequence, we prove the Kawamata-Viehweg vanishing theorem for klt del Pezzo surfaces of large characteristic.Comment: v2: final version. To appear in Compositio Mathematic

On base point free theorem for log canonical threefolds over the algebraic closure of a finite field

We prove the base point free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field.Comment: 20 pages. This is the final version, incorporating the referee's suggestion