La structure des courbes analytiques

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.

arXiv commentFrench, 357 p

Cited by in corpus (8)

• On the structure of nonarchimedean analytic curves
• Normalized Berkovich spaces and surface singularities
• Balancing conditions in global tropical geometry
• The convergence Newton polygon of a $p$-adic differential equation V : local index theorems
• Galois descent of semi-affinoid spaces
• Triangulations of non-archimedean curves, semi-stable reduction, and ramification
• Dynamique analytique sur $\mathbf{Z}$. I : Mesures d'équilibre sur une droite projective relative
• Schottky spaces and universal Mumford curves over $\mathbb{Z}$