8–11 juil. 2019
Université de Lille
Fuseau horaire Europe/Paris

Overconvergent cohomology and automorphic p-adic L-functions

9 juil. 2019, 15:30
1h
Salle de réunion (Université de Lille)

Salle de réunion

Université de Lille

Département de Mathématiques Cité Scientifique – Bâtiment M2 59655 Villeneuve d'Ascq Cedex France

Orateur

Daniel Barrera (Universidad de Santiago de Chile)

Description

p-adic L-functions attached to automorphic representations and p-adic families of them, provide powerful tools to attack important problems such as Birch-Swinnerton-Dyer and Bloch-Kato conjetures. However, they are hard to construct and in fact beyond the case GL(2) the theory is poorly understood.

In this talk I will describe an approach based on the study of the overconvergent cohomology of locally symmetric spaces. This approach was introduced by G. Stevens in the nineties and the most general constructions available for GL(2) were based on it. Then I will describe an ongoing joint work with M. Dimitrov and C. Williams in which we construct p-adic L-functions for certain cuspidal automorphic representations of GL(2n) by the use of convergent cohomology. This construction extends previous results of Gehrmann/Dimitrov-Januszewski-Raghuram to the non-ordinary setting and allows variation in p-adic families.

Documents de présentation

Aucun document.