The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2012

The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves

Résumé

We study the variation of the convergence Newton polygon of a differential equation along a smooth Berkovich curve over a non-archimedean complete valued field of characteristic 0. Relying on work of the second author who investigated its properties on affinoid domains of the affine line, we prove that its slopes give rise to continuous functions that factorize by the retraction through a locally finite subgraph of the curve.

Dates et versions

hal-00804806 , version 1 (26-03-2013)

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Jérôme Poineau, Andrea Pulita. The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves. 2012. ⟨hal-00804806⟩
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