Abstract
We prove that the radii of convergence of the solutions of a p-adic differential equation over an affinoid domain X of the Berkovich affine line are continuous functions on X that factorize through the retraction of of X onto a finite graph . 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.
Citation
Andrea Pulita. "The convergence Newton polygon of a p-adic differential equation I: Affinoid domains of the Berkovich affine line." Acta Math. 214 (2) 307 - 355, 2015. https://doi.org/10.1007/s11511-015-0126-9
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