MINIMAL MODEL PROGRAM FOR SEMI-STABLE THREEFOLDS IN MIXED CHARACTERISTIC

In this paper, we study the minimal model theory for threefolds in mixed characteristic. As a generalization of a result of Kawamata, we show that the minimal model program (MMP) holds for strictly semi-stable schemes over an excellent Dedekind scheme V of relative dimension two without any assumption on the residue characteristics of V. We also prove that we can run a (KX/V + Delta)-MMP over Z, where pi: X -> Z is a projective birational morphism of Q-factorial quasi-projective V schemes and (X, Delta) is a three-dimensional dlt pair with Exc(pi) subset of [Delta].