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arXiv · 2101.06257

Slopes of $F$-isocrystals over abelian varieties

Marco D'Addezio
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Abstract

We prove that an $F$-isocrystal over an abelian variety defined over a perfect field of positive characteristic has constant slopes. This recovers and extends a theorem of Tsuzuki for abelian varieties over finite fields. Our proof exploits the theory of monodromy groups of convergent isocrystals.

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Marco D'Addezio. 2021-01-15. Slopes of $F$-isocrystals over abelian varieties. https://doi.org/10.4171/dm/910

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