Minimal slope conjecture of F-isocrystals

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 constitutions of filtrations other. We affirmatively solve the conjecture for curves and $$\overline{{\mathbb {Q}}}_p$$ -F-isocrystals varieties over finite fields.