Utilisation de l'aplatissement en g\'eom\'etrie de Berkovich
Algebraic Geometry
2026-04-29 v3
Abstract
In this article, we carry out the flattening techniques developped in a former work in order to ``embellish" a map between compact analytic spaces, to describe the structure of its image, getting this way a substitute for Chevalley's theorem in the non-archimedean setting, and finally to show that flatness in the world of Berkovich spaces amounts to naive flatness provided one works with local rings for the G-topology
Keywords
Cite
@article{arxiv.2304.02415,
title = {Utilisation de l'aplatissement en g\'eom\'etrie de Berkovich},
author = {Antoine Ducros},
journal= {arXiv preprint arXiv:2304.02415},
year = {2026}
}
Comments
51 pages, French; this is the final version, to appear in Annales de l'institut Fourier