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

Article

Globally

+

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

Bhargav Bhatt ¹; Linquan Ma ¹; Zsolt Patakfalvi ¹; Karl Schwede ¹; Kevin Tucker ¹; Joe Waldron ¹; Jakub Witaszek ¹

¹

Publications Mathématiques de l'IHÉS, Volume 138 (2023), pp. 69-227

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.

Received: 2021-06-16
Accepted: 2023-04-12
Online First: 2023-05-10
Published online: 2023-12-07

MR Zbl

DOI: 10.1007/s10240-023-00140-8

Author's affiliations:

Bhargav Bhatt ¹; Linquan Ma ¹; Zsolt Patakfalvi ¹; Karl Schwede ¹; Kevin Tucker ¹; Joe Waldron ¹; Jakub Witaszek ¹

¹

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     author = {Bhargav Bhatt and Linquan Ma and Zsolt Patakfalvi and Karl Schwede and Kevin Tucker and Joe Waldron and Jakub Witaszek},
     title = {Globally $+$-regular varieties and the minimal model program for threefolds in mixed characteristic},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {69--227},
     year = {2023},
     publisher = {Springer International Publishing},
     address = {Cham},
     volume = {138},
     doi = {10.1007/s10240-023-00140-8},
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%A Linquan Ma
%A Zsolt Patakfalvi
%A Karl Schwede
%A Kevin Tucker
%A Joe Waldron
%A Jakub Witaszek
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Bhargav Bhatt; Linquan Ma; Zsolt Patakfalvi; Karl Schwede; Kevin Tucker; Joe Waldron; Jakub Witaszek. Globally $+$-regular varieties and the minimal model program for threefolds in mixed characteristic. Publications Mathématiques de l'IHÉS, Volume 138 (2023), pp. 69-227. doi: 10.1007/s10240-023-00140-8

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