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Varieties in positive characteristic with numerically flat log cotangent bundle

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arxiv 2303.09894 v1 pith:LOWTFT7U submitted 2023-03-17 math.AG

Sho Ejiri , Shou Yoshikawa This is my paper · ORCID
classification math.AG
keywords varietybundleflatnumericallycharacteristiccotangentprojectiveprove
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abstract

In this paper, we prove that a smooth projective globally $F$-split variety with numerically flat tangent bundle is an \'etale quotient of an ordinary abelian variety. We also show its logarithmic analog, which contains a characterization of toric varieties. We further prove that, without assumption of global $F$-splitting, a smooth projective separably rationally connected variety of arbitrary characteristic with numerically flat log cotangent bundle is a toric variety.

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  1. Quasi-canonical lifting of projective varieties in positive characteristic

    math.AG 2025-06 conditional novelty 7.0 of 10

    A descent theorem: a finite étale cover with a quasi-canonical lifting, of degree prime to p, forces the base variety to have a canonical lifting over the Witt vectors.

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