On the cuspidal divisor class group of a Drinfeld modular curve.
On the ...-factor attached to motives.
On the singular Drinfeld modules of rank 2.
On the torsion of the Mordell-Weil group of the Jacobian of Drinfeld modular curves.
P-Adic Homogeneous Spaces and Moduli Problems.
Problème de Lehmer en caractéristique finie
Problèmes diophantiens sur les -modules
On montre ici comment un raffinement de la hauteur canonique sur les puissances tensorielles du module de Carlitz permet d'obtenir des résultats de finitude pour les systèmes d'équations de Fermat. Ces résultats améliorent ceux de [D2]. On établit également une majoration de la différence entre la hauteur canonique et la hauteur de Weil sur les modules de Drinfeld. On termine en indiquant une liste de problèmes ouverts analogues aux conjectures diophantiennes de Lang, Mazur, Lehmer, et au théorème...
Quasi-periodic functions and Drinfeld modular forms
Relèvement selon une isogénie de système l-adiques de représentations galoisiennes associés aux motifs.
Shtukas and Jacobi sums.
Singular moduli and supersingular moduli of Drinfeld modules.
Stickelberger elements in function fields
Sur la géométrie de certaines algèbres de quaternions
Tensor products of drinfeld modules and v-adic representations.
The Drinfeld Modular Jacobian has connected fibers
We study the integral model of the Drinfeld modular curve for a prime . A function field analogue of the theory of Igusa curves is introduced to describe its reduction mod . A result describing the universal deformation ring of a pair consisting of a supersingular Drinfeld module and a point of order in terms of the Hasse invariant of that Drinfeld module is proved. We then apply Jung-Hirzebruch resolution for arithmetic surfaces to produce a regular model of which, after contractions in...
The Erdős and Halberstam theorems for Drinfeld modules of any rank (with an appendix by Hugh Thomas)
The formal completion of the Néron model of J0(p).
For any prime number p > 3 we compute the formal completion of the Néron model of J0(p) in terms of the action of the Hecke algebra on the Z-module of all cusp forms (of weight 2 with respect to Γ0(p)) with integral Fourier development at infinity.
The Mumford-Tate group of 1-motives
In this paper we study the structure and the degeneracies of the Mumford-Tate group of a 1-motive defined over . This group is an algebraic - group acting on the Hodge realization of and endowed with an increasing filtration . We prove that the unipotent radical of , which is , injects into a “generalized” Heisenberg group. We then explain how to reduce to the study of the Mumford-Tate group of a direct sum of 1-motives whose torus’character group and whose lattice are both of rank 1....
The refined p-adic abelian Stark conjecture in function fields.
Théorème de Lindemann-Weierstrass pour les modules de Drinfeld