Slopes of $F$-isocrystals over abelian varieties
Algebraic Geometry
2025-04-14 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.2101.06257,
title = {Slopes of $F$-isocrystals over abelian varieties},
author = {Marco D'Addezio},
journal= {arXiv preprint arXiv:2101.06257},
year = {2025}
}
Comments
8 pages; final version, to appear in Documenta Mathematica