Oratrices et orateurs et résumés > Tsuzuki Nobuo

Let ${\mathcal M}^\dagger$ and ${\mathcal N}^\dagger$ be overconvergent F-isocrystals admitting slope filtrations as convergent F-isocrystals on a smooth variety over a perfect field k of charactersitic p>0. K.S.Kedlaya asked a question: if the first step of slope filtration of $\mathcal M^\dagger$ is isomorphic to that of ${\mathcal N}^\dagger$, then ${\mathcal M}^\dagger$ and ${\mathcal N}^\dagger$ are isomorphic.

In this talk we prove Kedlaya's question in the case of curves (M.D'Addezio has affirmatively solved the problem in general recently). We study generic bounded solutions and their slopes of F-isocrystals, and explain our key notion ``PBQ" F-isocrystals on curves. For local objects, this notion was introduced by B.Chiarellotto and the speaker to study Dwork's conjecture on log-growth of solutions.