Marco d'Addezio

Title: Parabolicity conjecture of F-isocrystals

Abstract: 
We will present recent developments in the theory of overconvergent F-isocrystals, the p-adic 
analogue of ell-adic lisse sheaves. For the most part of the talk, we will explain a new result 
for the algebraic monodromy groups of these objects, namely the parabolicity conjecture. This is 
proven thanks to the study of the dagger-hull of F-isocrystals, a new concept introduced by the 
speaker. At the end of the talk, we will also mention an application of the theorem to the 
finiteness of separable p-torsion points of an abelian variety.