论文标题
混合特性中半稳定三倍的最小模型程序
Minimal model program for semi-stable threefolds in mixed characteristic
论文作者
论文摘要
在本文中，我们研究了混合特征中三倍的最小模型理论。作为Kawamata结果的概括，我们表明，MMP在一个出色的Dedekind方案$ V $的相对尺寸二的出色的Dedekind Schemes $ v $二的情况下，没有任何假设对$ v $的残留特性。我们还证明，我们可以在$ z $上运行$（k_ {x/v}+δ）$ - mmp-mmp，其中$π\ colon x \ to z $是$ \ mathbb {q} $ - fortorial quasi-projective quasi-projective quasi-projective quasi-projective $ v $ v $ -schemes and $（x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x，x的$ \ mathrm {ecc}（π）\ subset \lfloorΔ\ rfloor $。
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 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 $(K_{X/V}+Δ)$-MMP over $Z$, where $π\colon X \to Z$ is a projective birational morphism of $\mathbb{Q}$-factorial quasi-projective $V$-schemes and $(X,Δ)$ is a three-dimensional dlt pair with $\mathrm{Exc}(π) \subset \lfloor Δ\rfloor $.
