This paper resolves several outstanding questions regarding the Minimal Model Program for klt threefolds in mixed characteristic. Namely termination for pairs which are not pseudo-effective, finiteness of minimal models and the Sarkisov Program.

Fix a prime number p. We report on some recent developments in algebraic geometry (broadly construed) over p-adically complete commutative rings. These developments include foundational advances… Expand

I study the existence of log minimal models for a Kawamata log-terminal pair of relative dimension two over a Dedekind domain. This generalizes the semistable result of Kawamata. Also I prove a… Expand

A result by Birkar-Cascini-Hacon-McKernan together with the boundedness of length of extremal rays implies that different minimal models can be connected by a sequence of flops. A flop of a pair (X,… Expand

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… Expand