La structure des courbes analytiques

TL;DR

This paper explores the structure of Berkovich analytic curves, introduces a new proof of the semi-stable reduction theorem using triangulations, and aims to deepen understanding of non-Archimedean geometry.

Contribution

It provides a new proof of the semi-stable reduction theorem based on local analysis of Berkovich curves and formalizes the concept of triangulations.

Findings

New proof of semi-stable reduction theorem

Formalism of triangulations for Berkovich curves

Enhanced understanding of curve structures in non-Archimedean geometry

Abstract

This is a work in progress, far from being in its final form whose purpose is to investigate thoroughly the structure of Berkovich analytic curves and its relation with the semi-stable reduction theorem (of which a new proof is given here, starting from the local study of Berkovich curves) through the formalism of "triangulations". It has been already on the author's webpage for years, but it seems better to make it available on a public preprint server.