Jérôme Poineau

activity

20122024

most citedThe convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves

13 citations · 21 across the 12 of their papers we have counts for

collaborators

13 papers

math.NT2024

The convergence Newton polygon of a $p$ -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 $p$ -adic analytic curves. We showed t…

math.AG2023

Affine vs. Stein in rigid geometry

Marco Maculan, Jérôme Poineau

We investigate the relationship between affine and Stein varieties in the context of rigid geometry. We show that the two concepts are much more closely related than in complex geo…

math.AG2021

Schottky spaces and universal Mumford curves over $Z$

Jérôme Poineau, Daniele Turchetti

For every integer $g \geq 1$ we define a universal Mumford curve of genus $g$ in the framework of Berkovich spaces over $Z$ . This is achieved in two steps: first, we build…

math.AG2020★ 1 cited

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…

math.AG2018★ 1 cited

Definable sets of Berkovich curves

Pablo Cubides Kovacsics, Jérôme Poineau

In this article, we functorially associate definable sets to $k$ -analytic curves, and definable maps to analytic morphisms between them, for a large class of $k$ -analytic curves. G…

math.AG2017

Notions of Stein spaces in non-archimedean geometry

Marco Maculan, Jérôme Poineau

Let $k$ be a non-archimedean complete valued field and $X$ be a $k$ -analytic space in the sense of Berkovich. In this note, we prove the equivalence between three properties: 1) fo…

math.AG2017

On the number of connected components of the ramification locus of a morphism of Berkovich curves

Velibor Bojković, Jérôme Poineau

Let $k$ be a complete, nontrivially valued non-archimedean field. Given a finite morphism of quasi-smooth $k$ -analytic curves that admit finite triangulations, we provide upper bou…

math.NT2017

Pushforwards of $p$ -adic differential equations

Velibor Bojković, Jérôme Poineau

Given a differential equation on a smooth $p$ -adic analytic curve, one may construct a new one by pushing forward by an étale morphism. The main result of the paper provides an exp…

math.NT2013★ 6 cited

The convergence Newton polygon of a $p$ -adic differential equation V : local index theorems

Jérôme Poineau, Andrea Pulita

In this paper and its sequel we consider locally-free $O_{X}$ -modules together with a connection over a quasi-smooth Berkovich curve $X$ . We obtain necessary and sufficient…

math.NT2013

The convergence Newton polygon of a $p$ -adic differential equation III : global decompositions

Jérôme Poineau, Andrea Pulita

We deal with locally free $O_{X}$ -modules with connection over a Berkovich curve $X$ . As a main result we prove local and global decomposition theorems of such objects by t…

math.NT2012

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…

math.NT2012★ 13 cited

The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves

Jérôme Poineau, Andrea Pulita

We study the variation of the convergence Newton polygon of a differential equation along a smooth Berkovich curve over a non-archimedean complete valued field of characteristic 0.…

math.AG2012

Polynomial approximation of Berkovich spaces and definable types

Jérôme Poineau

We investigate affine Berkovich spaces over maximally complete fields and prove that they may be approximated by simpler spaces when the only functions we need to evaluate are poly…

The convergence Newton polygon of a p-adic differential equation IV : controlling graphs

Affine vs. Stein in rigid geometry

Schottky spaces and universal Mumford curves over Z

Berkovich curves and Schottky uniformization

Definable sets of Berkovich curves

Notions of Stein spaces in non-archimedean geometry

On the number of connected components of the ramification locus of a morphism of Berkovich curves

Pushforwards of p-adic differential equations

The convergence Newton polygon of a p-adic differential equation V : local index theorems

The convergence Newton polygon of a p-adic differential equation III : global decompositions

Continuity and finiteness of the radius of convergence of a p-adic differential equation via potential theory

The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves

Polynomial approximation of Berkovich spaces and definable types

The convergence Newton polygon of a $p$ -adic differential equation IV : controlling graphs

Schottky spaces and universal Mumford curves over $Z$

Pushforwards of $p$ -adic differential equations

The convergence Newton polygon of a $p$ -adic differential equation V : local index theorems

The convergence Newton polygon of a $p$ -adic differential equation III : global decompositions