Acta Mathematica

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

Jérôme Poineau and Andrea Pulita

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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.

Article information

Source
Acta Math. Volume 214, Number 2 (2015), 357-393.

Dates
Received: 3 June 2014
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485802424

Digital Object Identifier
doi:10.1007/s11511-015-0127-8

Zentralblatt MATH identifier
1332.12012

Subjects
Primary: 12H25: $p$-adic differential equations [See also 11S80, 14G20]
Secondary: 14G22: Rigid analytic geometry

Keywords
$p$-adic differential equations Berkovich spaces Radius of convergence Newton polygon continuity finiteness universal points extension of scalars

Rights
2015 © Institut Mittag-Leffler

Citation

Poineau, Jérôme; Pulita, Andrea. The convergence Newton polygon of a p -adic differential equation II: Continuity and finiteness on Berkovich curves. Acta Math. 214 (2015), no. 2, 357--393. doi:10.1007/s11511-015-0127-8. https://projecteuclid.org/euclid.acta/1485802424


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References

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