The weak Beauville--Bogomolov decomposition in characteristic p≥ 0

2019/12/29 by Zsolt Patakfalvi, Patakfalvi, Zsolt, Maciej Zdanowicz +1 · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1912.12742

Abstract

We prove a variant of the Beauville--Bogomolov decomposition for weakly ordinary, or generally globally F-split, varieties X with K_X ∼ 0, in characteristic p>0. We also show that the weakly ordinary assumption in our statement cannot be dropped. Additionally, if the assumption K_X ∼ 0 is replaced by -K_X being semi-ample, we show the weaker statement that all closed fibers of the Albanese morphism are isomorphic. Finally, we apply our main theorem to draw consequences to the behavior of rational points and fundamental groups of weakly ordinary K-trivial varieties in positive characteristic.

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• Varieties with nef anticanonical divisors and Albanese morphisms of relative dimension one in positive characteristic
• On asymptotic base loci of relative anti-canonical divisors of algebraic fiber spaces
• Moret-Bailly families and non-liftable schemes

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