Minimal slope conjecture of $F$-isocrystals

Abstract

The minimal slope conjecture, which was proposed by K.Kedlaya, asserts that two irreducible overconvergent $F$-isocrystals on a smooth variety are isomorphic to each other if both minimal slope constitutions of slope filtrations are isomorphic to each other. We affirmatively solve the minimal slope conjecture for overconvergent $F$-isocrystals on curves and for overconvergent ${\bar{\mathbb{Q}}}_p$-$F$-isocrystals on smooth varieties over finite fields.

Change of the proofs of 5.2 and 6.1

Cited by in corpus (1)

• Maximal tori of monodromy groups of $F$-isocrystals and an application to abelian varieties