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

Jérôme Poineau Laboratoire de mathématiques Nicolas Oresme, Université de Caen Andrea Pulita Département de mathématiques, Université de Montpellier II, CC051

Analysis of PDEs mathscidoc:1701.03013

Acta Mathematica, 214, (2), 357-393, 2014.6
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.
Berkovich spaces; Radius of convergence; Newton polygon; continuity; finiteness; universal points; extension of scalars
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@inproceedings{jérôme2014the,
  title={The convergence Newton polygon of a$p$-adic differential equation II: Continuity and finiteness on Berkovich curves},
  author={Jérôme Poineau, and Andrea Pulita},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203405110900803},
  booktitle={Acta Mathematica},
  volume={214},
  number={2},
  pages={357-393},
  year={2014},
}
Jérôme Poineau, and Andrea Pulita. The convergence Newton polygon of a$p$-adic differential equation II: Continuity and finiteness on Berkovich curves. 2014. Vol. 214. In Acta Mathematica. pp.357-393. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203405110900803.
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