Appendix: proof of the Uniformity Conjecture
Abstract
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)].
Cite
@article{arxiv.1108.0821,
title = {Appendix: proof of the Uniformity Conjecture},
author = {Francesco Baldassarri},
journal= {arXiv preprint arXiv:1108.0821},
year = {2011}
}
Comments
This article has been withdrawn.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