The anabelian geometry of curves over finite fields

In this talk I will discuss a new result on the anabelian geometry of curves over finite fields, which reads as follows: one can reconstruct the isomorphy type of a hyperbolic curve over a finite field from the isomorphy type of its geometrically pro-Sigma arithmetic fundamental group where Sigma is a "large" set of prime integers.
This result proven jointly with Akio Tamagawa refines previous results by Tamagawa and Mochizuki.