This paper grew out of the invitation of J. Nicaise and J. Sebag to add a contribution to the proceedings of the conference “Motivic integration and its interactions with model theory and non-archimedean geometry” (ICMS, Edinburgh 2008) ; I thank them heartily for that.

I wrote this paper during a stay at the Institute for Advanced Study in Princeton whose winterish but warm atmosphere was extremly motivating. I acknowledge support of the Institut universitaire de France, as well of the National Science Foundation under agreement No. DMS-0635607.

During the writing of this paper, transatlantic e-contacts with A. Ducros have been immensely profitable. Besides him, I also wish to thank M. Baker and A. Thuillier for their interest and comments.