Une correspondance de Jacquet-Langlands p-adique

Contribution à la recherche d'information : une fonction de correspondance

RÉSUMÉ. Un Système de Recherche d’Information (SRI) dispose d’un modèle de recherche capable de déterminer le degré de similarité qui existe entre un document et une requête. Généralement, le mécanisme consiste à apparier les documents et la requête en utilisant une fonction de correspondance. Dans ce papier, nous proposons la définition d’une fonction de correspondance qui repose sur les terme...

On Jacquet–Langlands isogeny over function fields

Article history: Received 15 August 2010 Revised 31 December 2010 Accepted 3 January 2011 Available online xxxx Communicated by David Goss MSC: primary 11G18, 11G09 secondary 14H40

The Jacquet-Langlands correspondence via `-adic uniformization

THE JACQUET-LANGLANDS CORRESPONDENCE FOR GL2 Contents

1.1. Matching regular semisimple conjugacy classes. Let X(F ) = F × F×, viewed as the space of semisimple conjugacy classes in GL2(F ) via GL2(F ) → X(F ) sending γ 7→ (Tr(γ),det(γ)). Similarly we have D× → X(F ) sending γ′ 7→ (TrD/F (γ),NmD/F (γ′)), where TrD/F and NmD/F mean reduced trace and norm. For regular semisimple γ ∈ GL2(F ) and γ′ ∈ D×, we write γ ∼ γ′ if they have the same image in ...

The local Jacquet-Langlands correspondence via Fourier analysis

Let F be a locally compact non-Archimedean field, and let B/F be a division algebra of dimension 4. The JacquetLanglands correspondence provides a bijection between smooth irreducible representations π′ of B× of dimension > 1 and irreducible cuspidal representations of GL2(F ). We present a new construction of this bijection in which the preservation of epsilon factors is automatic. This is don...