The non-archimedean Corona problem
The cohomology of Monsky and Washnitzer
Differential equations in characteristic
Recent work on differential Galois theory
Revêtements étales d'une courbe de Mumford
La conjecture de la couronne en analyse complexe et p-adique
De Rham cohomology of affinoid spaces
-adic Whittaker groups
Rigid analytic spaces
Monodromie d’une équation différentielle -adique
Les fonctions thêta d'une courbe de Mumford
Espaces de Banach non archimédiens
Continuous derivations of valued fields
Etale coverings of a Mumford curve
Let the field be complete w.r.t. a non-archimedean valuation. Let be a Mumford curve, i.e. the irreducible components of the stable reduction of have genus 0. The abelian etale coverings of are constructed using the analytic uniformization and the theta-functions on . For a local field one rediscovers . Frey’s description of the maximal abelian unramified extension of the field of rational functions of .
Galois properties of linear differential equations
The class group of a one-dimensional affinoid space
A curve over a non-archimedean valued field is with respect to its analytic structure a finite union of affinoid spaces. The main result states that the class group of a one dimensional, connected, regular affinoid space is trivial if and only if is a subspace of . As a consequence, has locally a trivial class group if and only if the stable reduction of has only rational components.
Discrete groups, Mumford curves and Theta functions
Families of linear differential equations related to the second Painlevé equation
This paper is a sequel to [vdP-Sa] and [vdP]. The two classes of differential modules (0,-,3/2) and (-,-,3), related to PII, are interpreted as fine moduli spaces. It is shown that these moduli spaces coincide with the Okamoto-Painlevé spaces for the given parameters. The geometry of the moduli spaces leads to a proof of the Painlevé property for PII in standard form and in the Flaschka-Newell form. The Bäcklund transformations, the rational solutions and the Riccati solutions for PII are derived...
On p-adic monodromy.
Fibrés vectoriels semi-stables sur une courbe de Mumford.
Page 1 Next