2011/08/03 by Francesco Baldassarri, Baldassarri, Francesco
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.1108.0821
This article has been withdrawn. It has been renamed "Radius of convergence of p-adic differential connections: an application to the p-adic Rolle theorem", and is posted as arXiv:1108.1633v1 [math.NT]. It has not yet been decided whether or not it will become an appendix to Faber's paper
openalex publication_date 2011/08/03 · arxiv created 2011/08/18 · arxiv updated 2011/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Kedlaya's intrinsic generic radius of convergence of a differential module [Def. 9.4.7 in p-adic Differential Equations, Cambridge Studies in Adv. Math., vol. 125 (2010)].