Acta Mathematica

The convergence Newton polygon of a p-adic differential equation I: Affinoid domains of the Berkovich affine line

Andrea Pulita

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Abstract

We prove that the radii of convergence of the solutions of a p-adic differential equation ${\fancyscript{F}}$ over an affinoid domain X of the Berkovich affine line are continuous functions on X that factorize through the retraction of ${X\to\Gamma}$ of X onto a finite graph ${\Gamma\subseteq X}$. We also prove their super-harmonicity properties. This finiteness result means that the behavior of the radii as functions on X is controlled by a finite family of data.

Article information

Source
Acta Math. Volume 214, Number 2 (2015), 307-355.

Dates
Received: 26 May 2014
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485802423

Digital Object Identifier
doi:10.1007/s11511-015-0126-9

Zentralblatt MATH identifier
1332.12013

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 spectral radius controlling graph finiteness

Rights
2015 © Institut Mittag-Leffler

Citation

Pulita, Andrea. The convergence Newton polygon of a p -adic differential equation I: Affinoid domains of the Berkovich affine line. Acta Math. 214 (2015), no. 2, 307--355. doi:10.1007/s11511-015-0126-9. https://projecteuclid.org/euclid.acta/1485802423


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