{"paper":{"title":"Appendix: proof of the Uniformity Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Francesco Baldassarri","submitted_at":"2011-08-03T11:12:50Z","abstract_excerpt":"This paper originated as an appendix to the paper \"Topology and Geometry of the Berkovich Ramification Locus for Rational Functions, II\" by Xander Faber arXiv:1104.0943v2 [math.NT]. It may however be read independently. We prove a variant of Alain Robert's p-adic Rolle theorem, via the theory of the radius of convergence of p-adic connections and the theory of semistable reduction of p-adic curves. We carefully compare the present author's notion [Inv. Math. 182 (2010)] of radius of convergence, of a connection on a p-adic curve X, normalized by the choice of a semistable model of X, with Kedl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0821","kind":"arxiv","version":3},"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"}