## 229 Citations

A weighted stable trace formula I: Basic functions

- Mathematics
- 2020

We establish endoscopic and stable trace formulas whose discrete spectral terms are weighted by automorphic L-functions, by the use of basic functions that are incorporated into the global spectral…

Transfer relations in essentially tame local Langlands correspondence

- Mathematics
- 2012

Let F be a non-Archimedean local field and G be the general linear group GLn over F . Bushnell and Henniart described the essentially tame local Langlands correspondence of G(F ) using rectifiers,…

Sur certaines identités endoscopiques entre transformées de Fourier

- Mathematics
- 2005

The main geometric terms of the Arthur-Selberg trace formula are the weighted orbital integrals. An important problem is to express these distributions as images by transfer of analogous…

Transfer factors for Lie Algebras

- Mathematics
- 1999

Let G be a quasi-split connected reductive group over a local field of characteristic 0, and fix a regular nilpotent element in the Lie algebra g of G. A theorem of Kostant then provides a canonical…

Rigid inner forms over local function fields

- Mathematics
- 2020

We generalize the concept of rigid inner forms, defined by Kaletha in [Kal16], to the setting of a local function field $F$ in order state the local Langlands conjectures for arbitrary connected…

On descent and the generic packet conjecture

- Mathematics
- 2016

Abstract Suppose F is a p-adic field, and H 1 ${\mathrm{H}_{1}}$ is (a z-extension of) a group that is twisted endoscopic to a connected reductive quasi-split group G over F. Suppose G satisfies the…

The cohomology of semi-infinite Deligne–Lusztig varieties

- Mathematics
- 2016

Abstract We prove a 1979 conjecture of Lusztig on the cohomology of semi-infinite Deligne–Lusztig varieties attached to division algebras over local fields. We also prove the two conjectures of…

Endoscopic transfer of orbital integrals in large residual characteristic

- Mathematics
- 2015

This article constructs Shalika germs in the context of motivic integration, both for ordinary orbital integrals and $\kappa$-orbital integrals. Based on transfer principles in motivic integration…

G\'eom\'etrisation du lemme fondamental pour l'alg\`ebre de Hecke

- Mathematics
- 2015

This article is the third one of the series \cite{Bt1}-\cite{Bt2} on Hitchin-Frenkel-Ngo fibration and Vinberg semigroup. Ngo \cite{N} proved the fundamental lemma for Lie algebras in equal…

## References

SHOWING 1-10 OF 11 REFERENCES

STABLE TRACE FORMULA: CUSPIDAL TEMPERED TERMS

- Mathematics
- 1984

Consider a connected reductive group G over a number field F. For technical reasons we assume that the derived group of G is simply connected (see [L1]). in [L3] Langlands partially stabilizes the…

On principal values on p-adic manifolds

- Mathematics
- 1983

In the paper [L] a project for proving the existence of transfer factors for forms of SL(3), especially for the unitary groups studied by Rogawski, was begun, and it was promised that it would be…

Orbital Integrals on Forms of SL(3), I

- Mathematics
- 1983

If G is a reductive group over a local or global field then it is possible to attach to G the endoscopic groups studied by Shelstad ([16] and the references therein) and myself ([5]). Over the real…

Linear Algebraic Groups

- Mathematics
- 1981

A linear algebraic group over an algebraically closed field k is a subgroup of a group GL n (k) of invertible n × n-matrices with entries in k, whose elements are precisely the solutions of a set of…

L-Indistinguishability for SL(2)*

- Mathematics
- 1979

1. Introduction. The notion of L-indistinguishability, like many others current in the study of L-functions, has yet to be completely defined, but it is in our opinion important for

Les débuts d'une formule des traces stable

- Mathematics
- 1979

Bien qu'une formule des traces stable générale n'existe pas encore, des cas particuliers ont ´ etéétablis et les efforts faits pour la prouver ont menéà d'autres recherches moins provisoires. Il…

Stable conjugacy: definitions and lemmas

- Mathematics
- 1979

The purpose of the present note is to introduce some notions useful for applications of the trace formula to the study of the principle of functoriality, including base change, and to the study of…