Construire un noyau de la fonctorialité ? Le cas de l’induction automorphe sans ramification de GL_1 à GL_2

Abstract

The purpose of this work is to present a new adelic method for realising Langlands’ functoriality principle in the case of unramified automorphic induction from GL 1 to GL 2 on function fields. A kernel of functoriality is built on the product of the adelic groups GL 1 and GL 2 . It is some kind of “family” local version of the construction for global Whittaker models, which is classically used in the “converse theorems” of Weil and Piatetski-Shapiro. Essential use is made of the Fourier transform on adele groups and of the Poisson formula, just as in Tate’s thesis.