Journée d'Arithmétique

21 mars 2013

Laboratoire Paul Painlevé, Université Lille 1
Salle de Réunion, 1er étage, bâtiment M2


9:45-10:30 Café de bienvenue

10:30-11:30 Adrian Iovita (Université Concordia et Université de Padoue) : Modular sheaves and p-adic families of Hilbert modular forms.

This is joint work with F. Andreatta, G. Stevens and V. Pilloni in which we construct p-adic families of overconvergent, finite slope Hilbert modular cuspforms attached to a prime integer p>2 and a totally real number field F (in which p might be ramified).

Pause déjeuner

14:00-15:00 Vincent Pilloni (ENS Lyon, CNRS) : Modularité en poids 0.

En collaboration avec B. Stroh, nous démontrons la modularité de certaines représentations p-adiques impaires de dimension 2 des groupes de Galois des corps totalement réels, à poids de Hodge-Tate nuls. Ces résultats permettent en particulier d'achever la démonstration de la conjecture d'Artin dans ce contexte.

15:00-15:45 Pause café

15:45-16:45 Jeanine Van Order (EPFL) : Algebraicity and nonvanising of Rankin-Selberg central values.

The aim of this talk is to explain the subtle but powerful link between algebraicity results for critical/central values of automorphic L-functions and the nonvanishing of these values in families, particularly in the setting of Rankin-Selberg L-functions of GL(2) of a totally real number field. In particular, I will explain how a strategy involving p-adic L-functions can be used to reduce a natural generalization of Mazur's conjectures to the non-self dual setting to some relatively simple analytic estimates. If time permits, then I will also outline some applications (e.g. to bounding Mordell-Weil ranks) and open problems.