Tate duality and ramification of division algebras
The capacity pairing.
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.
The cohomology of local systems on p-adically uniformized varieties.
The cohomology of Monsky and Washnitzer
The cohomology of p-adic symmetric spaces.
The intrinsic Hodge theory of -adic hyperbolic curves.
The overconvergence of morphisms of etale -spaces on a local field
The -adic finite Fourier transform and theta functions.
The rank of étale cohomology of varieties over -adic or number fields
The rationality of the Poincaré series associated to the p-adic points on a variety.
The reduction of a double covering of a Mumford curve.
The Schottky-Jung theorem for Mumford curves
The Schottky-Jung proportionality theorem, from which the Schottky relation for theta functions follows, is proved for Mumford curves, i.e. curves defined over a non-archimedean valued field which are parameterized by a Schottky group.
The structure of proper rigid groups.
The universal vectorial Bi-extension and p-adic heights.
Théorèmes de division sur et applications
Théorie de Fontaine en égales caractéristiques
Les chtoucas locaux sont des analogues en égales caractéristiques des groupes -divisibles — par exemple on leur associe un module de Tate, qui est un module libre sur l’anneau d’entiers d’un corps local de caractéristique positive. Nous associons à un chtouca local une structure de Hodge (ou, plus précisément, une structure de Hodge-Pink), ce qui induit un morphisme de périodes analogue à celui construit par Rapoport et Zink. Pour les structures de Hodge-Pink définies sur une extension finie...
Théorie d'Iwasawa et hauteurs p-adiques.
Torsion points on Jacobians of quotients of Fermat curves and p-adic soliton theory.
Torsors under tori and Néron models
Let be a Henselian discrete valuation ring with field of fractions . If is a smooth variety over and a torus over , then we consider -torsors under . If is a model of then, using a result of Brahm, we show that -torsors under extend to -torsors under a Néron model of if is split by a tamely ramified extension of . It follows that the evaluation map associated to such a torsor factors through reduction to the special fibre. In this way we can use the geometry of the special...