Slopes of -isocrystals over abelian varieties
Marco D’Addezio
Sorbonne Université, Paris, France
![Slopes of $F$-isocrystals over abelian varieties cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-28-issue-1.png&w=3840&q=90)
Abstract
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.
Cite this article
Marco D’Addezio, Slopes of -isocrystals over abelian varieties. Doc. Math. 28 (2023), no. 1, pp. 1–9
DOI 10.4171/DM/910