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Tuesday, May 12, 2020 | History

3 edition of Local constants and the Tame Langlands correspondence found in the catalog.

Local constants and the Tame Langlands correspondence

Allen Moy

Local constants and the Tame Langlands correspondence

by Allen Moy

  • 39 Want to read
  • 12 Currently reading

Published .
Written in English


Edition Notes

Statementby Allen Moy.
Classifications
LC ClassificationsMicrofilm 83/1008 (Q)
The Physical Object
FormatMicroform
Paginationiii, 88 leaves.
Number of Pages88
ID Numbers
Open LibraryOL3275601M
LC Control Number83198618

  Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group SLn(F). It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for SLn(F) enhanced with an irreducible representation of an S-group and, on the other hand, the union of the spaces of irreducible admissible Cited by: The Local Langlands Conjecture for GL(2) Colin J. Bushnell, Guy Henniart (auth.) If F is a non-Archimedean local field, local class field theory can be viewed as giving a canonical bijection between the characters of the multiplicative group GL(1,F) of F and the characters of the Weil group of F.

By Langlands, and Deligne we know that the local constants are extendible functions. Therefore, to give an explicit formula of the local constant of an induced representation of a local Galois group of a non-Archimedean local field F of characteristic zero, we have to compute the lambda function λ K / F for a finite extension K / this paper, when a finite extension K / F is Galois, we Cited by: 1. THE JACQUET-LANGLANDS CORRESPONDENCE FOR GL 2 Contents 1. Local statement and examples 1 2. Global statement and examples 2 3. Proofs 3 References 7 We follow [1, x8] with some examples and details supplemented. 1. Local statement and examples Let F be a local eld of characteristic not 2. Let Dbe a quaternion algebra over F (unique up to File Size: KB.

This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the enormously influential local Langlands conjectures. The survey gives a precise and accessible formulation of many aspects of the conjectures, highlighting. Correspondence Management Solution The Correspondence Management Solution centralizes and manages the creation, assembly and delivery of secure, personalized, and interactive correspondences. It enables you to quickly assemble correspondence from both pre-approved and custom-authored content in a streamlined process from creation to archival.


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Local constants and the Tame Langlands correspondence by Allen Moy Download PDF EPUB FB2

In mathematics, the local Langlands conjectures, introduced by Langlands (, ), are part of the Langlands describe a correspondence between the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of correspondence is not a bijection in general.

In mathematics, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and ed by Robert Langlands (, ), it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and seen as the single biggest project in modern.

The essentially tame local Langlands correspondence, II: Totally ramified representations Article in Compositio Mathematica (4) July with 18 Reads How we measure 'reads'.

The local Langlands correspondence, which is known in the real case and partially constructed in the p-adic case, assigns to each Langlands parameter for a reductive group G over a local field F a Author: Geo Kam-Fai Tam.

$\begingroup$ A great example in this spirit is the Sp4 paper of Gan-Takeda that I referenced. They used L-functions in the generic case -- when suitable L-functions can be defined without LLC -- and Plancherel measure in the non-generic case -- when suitable L-functions are harder to define (though there are options using Bessel instead of Whittaker models).

(1) is there a geometric Langlands correspondence, at least in conjectural form, for reductive groups over archimedean local fields. (2) Does the formal affine line over an archimedean local field play a role in it, and if so, which role.

Perhaps, somehow (how?), in analogy with local class field theory. I'd appreciate some references. Refs. We extend our methods from Scholze (Invent. Math. doi: /sy) to reprove the Local Langlands Correspondence for GL n over p-adic fields as well as the existence of ℓ-adic Galois representations attached to (most) regular algebraic conjugate self-dual cuspidal automorphic representations, for which we prove a local-global compatibility statement as in the book Cited by: Roger Plymen The local Langlands correspondence for inner forms of SLn An associative algebra over a eld is a division algebra if and only if it has a multiplicative identity element 1 Cited by:   We provide the following remarks before the end of this section.

The existence of these two transfers are implied by the Fundamental Lemmas. When char $$(F)=0$$⁠, the lemma is proved by Waldspurger [] in the case of automorphic induction and by Arthur and Clozel [] in the case of base char $$(F)>0$$⁠, they are proved by Henniart and Lemaire [14, Théorème ; 15, Cited by: 4.

The goal of this book is to present a systematic and self-contained introduction to the local geometric Langlands Correspondence for loop groups and the related representation theory of affine Kac-Moody algebras.

It is partially based on the graduate courses taught by. 2 PETER SCHOLZE 1. Introduction The aim of this paper is to give a new proof of the Local Langlands Correspondence for GLnover p-adic fields, and to simplify some of the arguments in the book by Harris- Taylor, [10].

Fix a p-adic field F, i.e., a finite extension of Qp, with ring of integers O. Recall that the Local Langlands Correspondence, which is now a theorem due to Harris-Taylor, [10]. 2 PETER SCHOLZE 1. Introduction The aim of this paper is to give a new proof of the Local Langlands Correspondence for GL nover p-adic elds, and to simplify some of the arguments in the book by Harris- Taylor, [10].

Fix a p-adic eld F, i.e., a nite extension of QFile Size: KB. Abstract: The local Langlands correspondence for GL(n) of a non-Archimedean local field $F$ parametrizes irreducible admissible representations of $GL(n,F)$ in terms Cited by: [Moy] A. Moy, Local constants and the tame Langlands correspondence, Thesis, Univ.

of Chicago, Zentralblatt MATH: Mathematical Reviews (MathSciNet): MR [Novod] M. Novodvordsky, Automorphic L-functions for the symplectic group GS p (4), Proc. Sympos. MAXIMAL VARIETIES AND THE LLC 3 where ˇ0corresponds to ˇunder the local Jacquet-Langlands correspondence, ˇ 0is the contragredient of ˇ0and ˇ7!˙](ˇ) is a certain normalization (see Theorem C in x) of the local Langlands correspondence.

In other words, the degree n 1 cohomology of the FCited by:   A New Approach to the Local Langlands Correspondence for GLnGLn Over p-Adic Fields - Peter Scholze University of Bonn Novem We. Dans cet article, nous allons étudier le comportement des conjectures locales de Deligne-Langlands par réduction modulo un nombre premier l, dans quelques cas by: 9.

Daniels's The Correspondence is an epic in fragments: masterly, comic, wise, daring. It is a book for everyone, from Kentucky to Cambridge to Kathmandu, though as a reader you may feel that Daniels is trafficking in secrets, meant for you alone.

It is occult. It is so strong, it /5(16). MAXIMAL VARIETIES AND THE LLC 3 where ˇ0corresponds to ˇunder the local Jacquet-Langlands correspondence, ˇ 0is the contragredient of ˇ0and ˇ7!˙](ˇ) is a certain normalization (see Theorem C in x) of the local Langlands correspondence. In other words, the degree n Cited by: The local Langlands correspondence in families and Ihara’s lemma for U(n) Claus M.

Sorensen Abstract The goal of this paper is to reformulate the conjectural "Ihara lemma" for U(n) in terms of the local Langlands correspondence in families ~ˇ (), as currently being developed by Emerton and Helm.

The reformulation roughly takes the following Cited by: 3. Local constants and the tame Langlands correspondence Author(s): Moy, Allen Source: Amer.

Jour. of Math., v., p. – Year: Harish-Chandra homomorphisms for p-adic groups Author(s): Howe, Roger; Moy, Allen.This chapter discusses the discrete series characters for reductive p-adic discrete series, which is well understood for real groups, has presented one of the most vexing problems in the representation theory of p-adic has been some progress in the construction of discrete series ([Hi], [KL], [Kub]), but only a few results exist on the specific nature of their by: Ramifications of the Geometric Langlands Program 53 • At the points at which the connection has regular singularity (pole of order 1) one can take instead of the level structure, a parabolic structure, i.e., a reduction of the fiber of the bundle to a Borel subgroup of G.

• The Langlands correspondence will assign to a flat LG-bundle E =(F,∇) with ramification at the points y.