Globally + -regular varieties and the minimal model program for threefolds in mixed characteristic

Bhargav Bhatt; Linquan Ma; Zsolt Patakfalvi; Karl Schwede; Kevin Tucker; Joe Waldron; Jakub Witaszek

doi:10.1007/s10240-023-00140-8

Globally + -regular varieties and the minimal model program for threefolds in mixed characteristic

Bhargav Bhatt
, Linquan Ma
, Zsolt Patakfalvi
, Karl Schwede
, Kevin Tucker
, Joe Waldron
, Jakub Witaszek

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

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 characteristic and identify certain stable sections of adjoint line bundles. Finally, by passing to graded rings, we generalize a special case of Fujita’s conjecture to mixed characteristic.

Original language	English (US)
Pages (from-to)	69-227
Number of pages	159
Journal	Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume	138
Issue number	1
DOIs	https://doi.org/10.1007/s10240-023-00140-8
State	Published - Dec 2023

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s10240-023-00140-8

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abstract = "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 characteristic and identify certain stable sections of adjoint line bundles. Finally, by passing to graded rings, we generalize a special case of Fujita{\textquoteright}s conjecture to mixed characteristic.",

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AU - Schwede, Karl

AU - Tucker, Kevin

AU - Waldron, Joe

AU - Witaszek, Jakub

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AB - 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 characteristic and identify certain stable sections of adjoint line bundles. Finally, by passing to graded rings, we generalize a special case of Fujita’s conjecture to mixed characteristic.

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Globally + -regular varieties and the minimal model program for threefolds in mixed characteristic

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