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

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.

arXiv comment132 pages, numerous minor changes, corrections, more detailed explanations and expositional improvements

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• Covers of rational double points in mixed characteristic
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Cited by in corpus (12)

• Cohen-Macaulayness of absolute integral closures
• Minimal model program for semi-stable threefolds in mixed characteristic
• An analog of adjoint ideals and PLT singularities in mixed characteristic
• Resolution and alteration with ample exceptional divisor
• Relative semiampleness in mixed characteristic
• Relative MMP without Q-factoriality
• Coherence of absolute integral closures
• Moishezon Spaces and Projectivity Criteria
• On the termination of the MMP for semi-stable fourfolds in mixed characteristic
• On log minimality of weak K-moduli compactifications of Calabi-Yau varieties
• Mori Fibrations in Mixed Characteristic
• The minimal model program for arithmetic surfaces enriched by a Brauer class