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

2020/12/31 by Bhatt, Bhargav, Ma, Linquan, Patakfalvi, Zsolt +4
#11G99 #13A35 #13D22 #14B05 #14D10 #14E30 #14F18 #14J30 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2012.15801

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.

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