A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf II

Sho Ejiri; Akiyoshi Sannai

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arXiv · 1702.04209

A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf II

Sho Ejiri·Akiyoshi Sannai

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Abstract

In this paper, we prove that a smooth projective variety $X$ of characteristic $p>0$ is an ordinary abelian variety if and only if $K_X$ is pseudo-effective and $F^e_*\mathcal O_X$ splits into a direct sum of line bundles for an integer $e$ with $p^e>2$.

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BibTeX RIS

Sho Ejiri, Akiyoshi Sannai. 2017-02-14. A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf II. https://arxiv.org/abs/1702.04209

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