D\'evisser, d\'ecouper, \'eclater et aplatir les espaces de Berkovich

Abstract

We develop in this article flattening techniques for coherent sheaves in the realm of Berkovich spaces; we are inspired by the general strategy that Raynaud and Gruson have used for dealing with the analogous problem in scheme theory. As an application, we give a general description of the image of an arbitrary morphism between compact analytic spaces.