Globally <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>+</mml:mo> </mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> </mml:math> -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.