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

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Acta Mathematica

Abstract

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 zero. 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 factorise by the retraction through a locally finite subgraph of the curve.

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Authors and Affiliations

  1. Laboratoire de mathématiques Nicolas Oresme, Université de Caen, BP 5186, FR-14032, Caen Cedex, France

    Jérôme Poineau

  2. Département de mathématiques, Université de Montpellier II, CC051, Place Eugène Bataillon, FR-34095, Montpellier Cedex 5, France

    Andrea Pulita

Authors
  1. Jérôme Poineau
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  2. Andrea Pulita
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Correspondence to Andrea Pulita.

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Poineau, J., Pulita, A. The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves. Acta Math 214, 357–393 (2015). https://doi.org/10.1007/s11511-015-0127-8

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  • DOI: https://doi.org/10.1007/s11511-015-0127-8

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