Continuity and finiteness of the radius of convergence of a p-adic differential equation via potential theory

2012/09/27 by Jérôme Poineau, Poineau, Jérôme, Andréa Pulita +2
Mathematics · #12H25 #14G22 #Advanced Harmonic Analysis Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:12H25 #msc:14G22

paper · pdf · doi:10.48550/arxiv.1209.6276

20 pages

arxiv created 2012/09/27 · openalex publication_date 2012/09/27 · arxiv updated 2012/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the radius of convergence of a differential equation on a smooth Berkovich curve over a non-archimedean complete valued field of characteristic 0. Several properties of this function are known: F. Baldassarri proved that it is continuous and the authors showed that it factorizes by the retraction through a locally finite graph. Here, assuming that the curve has no boundary or that the differential equation is overconvergent, we provide a shorter proof of both results by using potential theory on Berkovich curves.

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