Les espaces de Berkovich sont mod\'er\'es, d'apr\`es E. Hrushovski et F. Loeser

Abstract

This is the (revised) printed version of the talk no 1056 (june 2012) of the Bourbaki seminar, which will be published in an Ast\'erisque volume. This is a report on a paper by Hrushovski and Loeser (/arxiv:1009.0252). In this paper they establish, using in a crucial way model-theoretic tools and especially the notion of a stably dominated type, various tameness properties of the topology of algebraic Berkovich spaces (e.g. they prove that such a space has the homotopy type of a compact polyhedron).