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arXiv · 1208.5850

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 $\mathcal{F}$ 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. Roughly speaking, this finiteness result means that the behavior of the radii as functions on $X$ is controlled by a finite family of data.

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Andrea Pulita. 2012-08-29. The convergence Newton polygon of a $p$-adic differential equation I : Affinoid domains of the Berkovich affine line. https://arxiv.org/abs/1208.5850

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