Appendix: proof of the Uniformity Conjecture

Details Appendix: proof of the Uniformity Conjecture Appendix: proof of the Uniformity Conjecture

2011-08-03

arxiv.org/abs/1108.0821v3

Mathematics

Number Theory

This article has been withdrawn. It has been renamed "Radius of convergence of p-adic differential connections: an application

Scientific paper

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)].

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