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

• 成果类型: Article
• 署名作者: Pulita, Andrea
• 署名单位: Universite de Montpellier
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-015-0126-9
• 发表日期: 2015
• 页码: 307-355
• 关键词: flat meromorphic connections; index theorem; local monodromy; Operators; irregularity; coefficients; continuity; EXTENSIONS; CURVES

摘要

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.