Slopes of -isocrystals over abelian varieties

  • Marco D’Addezio

    Sorbonne Université, Paris, France
Slopes of $F$-isocrystals over abelian varieties cover
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We prove that an -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, Slopes of -isocrystals over abelian varieties. Doc. Math. 28 (2023), no. 1, pp. 1–9

DOI 10.4171/DM/910