Analytic continuation of representations and estimates of automorphic forms.
We study the irreducible constituents of the reduction modulo of irreducible algebraic representations of the group for a finite extension of . We show that asymptotically, the multiplicity of each constituent depends only on the dimension of and the central character of its reduction modulo . As an application, we compute the asymptotic value of multiplicities that are the object of the Breuil-Mézard conjecture.
We show that it is possible in rather general situations to obtain a finite-dimensional modular representation of the Galois group of a number field as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over , provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification...
We develop a new method to bound the hyperbolic and spherical Fourier coefficients of Maass forms defined with respect to arbitrary uniform lattices.
Soit un corps local non archimédien de caractéristique nulle et de caractéristique résiduelle impaire. On décrit explicitement les changements de base des représentations supercuspidales de . C’est une étape vers la description du changement de base des paquets endoscopiques supercuspidaux de .
The aim of these notes is to generalize Laumon’s construction [20] of automorphic sheaves corresponding to local systems on a smooth, projective curve to the case of local systems with indecomposable unipotent ramification at a finite set of points. To this end we need an extension of the notion of parabolic structure on vector bundles to coherent sheaves. Once we have defined this, a lot of arguments from the article “ On the geometric Langlands conjecture” by Frenkel, Gaitsgory and Vilonen [11]...