On the existence of flips for threefolds in mixed characteristic $(0,5)$

Abstract

We provide a detailed proof of the validity of the Minimal Model Program for threefolds over excellent Dedekind separated schemes whose residue fields do not have characteristic 2 or 3.

Termination of threefold flips in mixed characteristic

“…When the pair is pseudo-effective more is known, it is shown that in fact every MMP terminates without the need for scaling [2,Theorem 9.8]. Subsequent work in [12] establishes analogous results in the 𝑝 = 5 case. For the special case of semi-stable fibrations, [11] covers the case of semi-stable threefolds without constraint on the characteristic, while [4] and [13] show MMP's exist over Dedekind domains with perfect residue fields of characteristic 𝑝 > 5.…”