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In this article, we carry out the flattening techniques developped in aformer work in order to ``embellish" a map between compact analytic spaces, todescribe the structure of its image, getting this way a substitute forChevalley's theorem in the non-archimedean setting, and finally to show thatflatness in the world of Berkovich spaces amounts to naive flatness providedone works with local rings for the G-topology

Utilisation de l'aplatissement en g\'eom\'etrie de Berkovich