{"paper":{"title":"The convergence Newton polygon of a $p$-adic differential equation I : Affinoid domains of the Berkovich affine line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Pulita","submitted_at":"2012-08-29T07:00:20Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5850","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}