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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Minimal model program for semi-stable threefolds in mixed characteristic


Authors: Teppei Takamatsu and Shou Yoshikawa
Journal: J. Algebraic Geom. 32 (2023), 429-476
DOI: https://doi.org/10.1090/jag/813
Published electronically: March 24, 2023
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Abstract: 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 $(K_{X/V}+\Delta )$-MMP over $Z$, where $\pi \colon X \to Z$ is a projective birational morphism of $\mathbb {Q}$-factorial quasi-projective $V$-schemes and $(X,\Delta )$ is a three-dimensional dlt pair with $Exc(\pi ) \subset \lfloor \Delta \rfloor$.


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Teppei Takamatsu
Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
Email: teppeitakamatsu.math@gmail.com

Shou Yoshikawa
Affiliation: RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Wako, Saitama 351-0198, Japan
MR Author ID: 1456291
ORCID: 0000-0003-4262-0876
Email: shou.yoshikawa@riken.jp

Received by editor(s): April 15, 2021
Received by editor(s) in revised form: March 4, 2022, April 26, 2022, and July 1, 2022
Published electronically: March 24, 2023
Additional Notes: The first author was supported by the Program for Leading Graduate Schools, MEXT, Japan and JSPS KAKENHI Grant number JP19J22795. The second author was supported by the Program for Leading Graduate Schools, MEXT, Japan and JSPS KAKENHI Grant number JP19J22795.
Article copyright: © Copyright 2023 University Press, Inc.