4 papers
The convergence Newton polygon of a -adic differential equation IV : controlling graphs
Jérôme Poineau, Andrea Pulita
In our previous works we proved a finiteness property of the radii of convergence functions associated with a vector bundle with connection on -adic analytic curves. We showed t…
Schottky spaces and universal Mumford curves over
Jérôme Poineau, Daniele Turchetti
For every integer we define a universal Mumford curve of genus in the framework of Berkovich spaces over . This is achieved in two steps: first, we build…
Berkovich curves and Schottky uniformization
Jérôme Poineau, Daniele Turchetti
This text is an exposition of non-Archimedean curves and Schottky uniformization from the point of view of Berkovich geometry. It consists of two parts, the first one of an introdu…
Continuity and finiteness of the radius of convergence of a p-adic differential equation via potential theory
Jérôme Poineau, Andrea Pulita
We study the radius of convergence of a differential equation on a smooth Berkovich curve over a non-archimedean complete valued field of characteristic 0. Several properties of th…