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

Akiyoshi Sannai; Hiromu Tanaka

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arXiv · 1411.5294

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

Akiyoshi Sannai·Hiromu Tanaka

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Abstract

For an ordinary abelian variety $X$, $F^e_*\mathcal{O}_X$ is decomposed into line bundles for every positive integer $e$. Conversely, if a smooth projective variety $X$ satisfies this property and its Kodaira dimension is non-negative, then $X$ is an ordinary abelian variety.

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Akiyoshi Sannai, Hiromu Tanaka. 2014-11-19. A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf. https://arxiv.org/abs/1411.5294

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