On the effective generation of direct images of pluricanonical bundles in mixed characteristic

Abstract

We present an effective global generation result for direct images of pluricanonical bundles in mixed characteristic. This is a mixed characteristic analog of Ejiri's theorem in positive characteristic and the theorem of Popa and Schnell regarding their Fujita-type conjecture in characteristic zero. As an application, we establish a weak positivity statement for the relative canonical sheaf of a smooth morphism in mixed characteristic.

32 pages. Comments welcome. v3: Improved exposition throughout. v2: Edited Introduction