English

Slopes of $F$-isocrystals over abelian varieties

Algebraic Geometry 2025-04-14 v2 Number Theory

Abstract

We prove that an FF-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