Radius of convergence of p-adic connections and the Berkovich ramification locus
arXiv:1209.0081
Abstract
We apply the theory of the radius of convergence of a p-adic connection to the special case of the direct image of the constant connection via a finite morphism of compact p-adic curves, smooth in the sense of rigid geometry. In the case of an etale covering of curves with good reduction, we get a lower bound for that radius and obtain a new geometric proof of a variant of the p-adic Rolle theorem of Robert and Berkovich. We take this opportunity to clarify the relation between our notion of radius of convergencand the more intrinsic one used by Kedlaya
new version of arXiv:1108.1633v3. Michael Temkin informed us of a substantial error in the previous version of this paper. This is now corrected and the structure of the paper is very much simplified