# Questions on fundamental groups of arithmetic varieties

## Location

384H

Monday, May 1, 2023 2:30 PM

Francois Charles (ENS)

I will report on some questions and results regarding the étale fundamental groups of projective, regular schemes over the ring of integers of a number fields. In specific cases, I will explain how to use methods of formal-analytic geometry to prove finiteness results for those groups (joint with Jean-Benoît Bost), and I will describe general finiteness results for their representations.