The convergence Newton polygon of a p-adic differential equation I : Affinoid domains of the Berkovich affine line

2012/08/29 by Andréa Pulita, Pulita, Andrea · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · doi:10.48550/arxiv.1208.5850

openalex publication_date 2012/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the radii of convergence of the solutions of a p-adic differential equation F over an affinoid domain X of the Berkovich affine line are continuous functions on X that factorize through the retraction of X→Γ of X onto a finite graph Γ⊆ X. We also prove their super-harmonicity properties. Roughly speaking, this finiteness result means that the behavior of the radii as functions on X is controlled by a finite family of data.

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