The essentially tame Jacquet-Langlands correspondence for inner forms of GL(n)

Some Endoscopic Properties of The Essentially Tame Jacquet-Langlands Correspondence

Let F be a non-Archimedean local field of characteristic 0 and G be an inner form of the general linear group G = GLn over F . We show that the rectifying character appearing in the essentially tame Jacquet-Langlands correspondence of Bushnell and Henniart for G and G can be factorized into a product of some special characters, called zeta-data in this paper, in the theory of endoscopy of Langl...

On the Jacquet–Langlands correspondence for Hilbert modular forms

2 Modular forms and Automorphic forms 2 2.1 Modular Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The Adele group of GL2 over Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Automorphic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Hecke act...

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 Jacquet-Langlands correspondence via `-adic uniformization

A geometric Jacquet-Langlands correspondence for U(2) Shimura varieties

Let G be a unitary group over Q, associated to a CM-field F with totally real part F, with signature (1, 1) at all the archimedean places of F. For certain primes p, and X a Shimura variety associated to G with good reduction at p, we construct a stratification of the characteristic p fiber of X , whose closed strata are indexed by subsets S of the archimedean places of F. Certain closed strata...