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Pré-Publication, Document De Travail Année : 2012

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

Résumé

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.

Dates et versions

hal-00804808 , version 1 (26-03-2013)

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Jérôme Poineau, Andrea Pulita. Continuity and finiteness of the radius of convergence of a p-adic differential equation via potential theory. 2012. ⟨hal-00804808⟩
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