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

## TL;DR

This paper introduces flattening techniques for coherent sheaves on Berkovich spaces, inspired by scheme theory, and applies them to describe images of morphisms between compact analytic spaces.

## Contribution

It develops new flattening methods for coherent sheaves in Berkovich spaces, extending scheme theory techniques to non-Archimedean analytic geometry.

## Key findings

- Provides a general description of the image of morphisms between compact analytic spaces
- Introduces flattening techniques for coherent sheaves in Berkovich spaces
- Extends scheme-theoretic flattening strategies to non-Archimedean geometry

## 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.