Slopes of $F$-isocrystals over abelian varieties

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.

8 pages; final version, to appear in Documenta Mathematica

References in corpus (1)

• On the universal extensions in Tannakian categories