Minimal slope conjecture of F-isocrystals

Abstract

The minimal slope conjecture, which was proposed by K. S. 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 $$\overline{{\mathbb {Q}}}_p$$ -F-isocrystals on smooth varieties over finite fields.