Géométrie anabélienne tempérée

Abstract

The tempered fundamental group of a p-adic analytic variety classifies étale coverings that become topological coverings (for the Berkovich topology) after finite étale base change. I study what can be recovered from the tempered fundamental group. In particular, I prove that, for a Mumford curve, one can recover the metric of the graph of the stable reduction from the tempered fundamental group. I also study how the tempered fundamental group behaves along the fibers of a fibration.

PhD thesis; french