A Nonvanishing Theorem for the Cuspidal Cohomology of SL2 Over Imaginary Quadratic Integers.
A note on the global Langlands conjecture.
A relation between automorphic representations of and
A remark on Construire un noyau de la fonctorialité by Lafforgue
Lafforgue has proposed a new approach to the principle of functoriality in a test case, namely, the case of automorphic induction from an idele class character of a quadratic extension. For technical reasons, he considers only the case of function fields and assumes the data is unramified. In this paper, we show that his method applies without these restrictions. The ground field is a number field or a function field and the data may be ramified.
A remark on my paper "On the Saito-Kurokawa lifting".
Analytical construction of Weil curves over function fields
Artin -functions and normalization of intertwining operators
Automorphic vector bundles on connected Shimura varieties.
Changement du corps de base pour les représentations de
Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems
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]...
Cohomologie d’intersection et fonctions de certaines variétés de Shimura
Cohomologie, -groupes et fonctorialité
Compatibility of the theta correspondence with the Whittaker functors
We prove that the global geometric theta-lifting functor for the dual pair is compatible with the Whittaker functors, where is one of the pairs , or . That is, the composition of the theta-lifting functor from to with the Whittaker functor for is isomorphic to the Whittaker functor for .
Construire un noyau de la fonctorialité ? Le cas de l’induction automorphe sans ramification de GL à GL
Le but de cet article est de présenter une nouvelle méthode purement adélique pour réaliser le principe de fonctorialité de Langlands dans le cas de l’induction automorphe sans ramification de GL à GL sur les corps de fonctions. On construit sur le produit des groupes adéliques GL et GL un noyau de la fonctorialité. C’est une version “en famille” et locale de la construction par les modèles de Whittaker globaux, utilisée classiquement dans les “théorèmes réciproques” de Weil et Piatetski-Shapiro....
Diedergruppe und Reziprozitätsgesetz.
Formes de Maass et représentations galoisiennes
Functional equation satisfied by certain -functions
Geometric theta-lifting for the dual pair
Let be a smooth projective curve over an algebraically closed field of characteristic . Consider the dual pair over with split. Write and for the stacks of -torsors and -torsors on . The theta-kernel on yields theta-lifting functors and between the corresponding derived categories. We describe the relation of these functors with Hecke operators. In two particular cases these functors realize the geometric Langlands functoriality for the above pair (in the non ramified case)....
Global -packets for GSp(2) and theta lifts.
Höhere Reziprozitätsgesetze und Modulformen vom Gewicht Eins.