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

We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global F -regularity to mixed characteristic and identify certain stable sections of adjoint line bundles. Finally, by passing to graded rings, we generalize a special case of Fujita's conjecture to mixed characteristic.

No abstract

We show the validity of the relative dlt MMP over Qfactorial threefolds in all characteristics p > 0. As a corollary, we generalise many recent results to low characteristics including: W Orationality of klt singularities, inversion of adjunction, normality of divisorial centres up to a universal homeomorphism, and the existence of rational points on log Fano threefolds.

No abstract