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.

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

References in corpus (6)

• Termination of (many) 4-dimensional log flips
• The Minimal Model Program for threefolds in characteristic five
• Minimal model program for semi-stable threefolds in mixed characteristic
• Vanishing theorems for threefolds in characteristic $p>5$
• Relative MMP without Q-factoriality
• Nakai--Moishezon ampleness criterion for real line bundles

Cited by in corpus (10)

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