Les espaces de Berkovich sont modérés, d'après E. Hrushovski et F. Loeser

Antoine Ducros

Published 2012-10-16Version 1

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).