The Uniform Position Principle for Curves in Characteristic p.
The universal tropicalization and the Berkovich analytification
Given an integral scheme over a non-archimedean valued field , we construct a universal closed embedding of into a -scheme equipped with a model over the field with one element (a generalization of a toric variety). An embedding into such an ambient space determines a tropicalization of by previous work of the authors, and we show that the set-theoretic tropicalization of with respect to this universal embedding is the Berkovich analytification . Moreover, using the scheme-theoretic...
The universal vectorial Bi-extension and p-adic heights.
The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces
We study the functional codes defined on a projective algebraic variety , in the case where is a non-degenerate Hermitian surface. We first give some bounds for , which are better than the ones known. We compute the number of codewords reaching the second weight. We also estimate the third weight, show the geometrical structure of the codewords reaching this third weight and compute their number. The paper ends with a conjecture on the fourth weight and the fifth weight of the code .
The work of Gross and Zagier on Heegner points and the derivatives of -series
The work of Mazur and Wiles on cyclotomic fields
Théorème de Hilbert-Samuel «arithmétique»
On donne une nouvelle démonstration directe du théorème de Hilbert-Samuel arithmétique et on déduit un critère numérique pour l’existence de sections d’un fibré en droite sur une variété arithmétique de norme sup inférieure à un.
Théorèmes d'algébricité en géométrie diophantienne
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 de Kummer sur les groupes algébriques
Théorie de l'intersection et théorème de Riemann-Roch arithmétiques
Théorie d'Iwasawa et hauteurs p-adiques.
Theta height and Faltings height
Using original ideas from J.-B. Bost and S. David, we provide an explicit comparison between the Theta height and the stable Faltings height of a principally polarized Abelian variety. We also give as an application an explicit upper bound on the number of -rational points of a curve of genus under a conjecture of S. Lang and J. Silverman. We complete the study with a comparison between differential lattice structures.
Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper.
Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper. II.
Three constructions of rational points on Y2 = X3 ... NX.
Three constructions of rational points on Y2 = X3 ... NX (Errata).
Three-dimensional hyperbolic geometry as ...-adic Arakelov geometry.
Thue equations over algebraic function fields