Around Langlands Correspondences
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Author | : Farrell Brumley |
Publisher | : American Mathematical Soc. |
Total Pages | : 394 |
Release | : 2017 |
Genre | : Mathematics |
ISBN | : 147043573X |
Download Around Langlands Correspondences Book in PDF, Epub and Kindle
Presents, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers.
Author | : Farrell Brumley |
Publisher | : |
Total Pages | : 394 |
Release | : 2017 |
Genre | : Algebraic number theory |
ISBN | : 9781470441173 |
Download Around Langlands Correspondences Book in PDF, Epub and Kindle
This volume contains the proceedings of the international conference "Around Langlands Correspondences", held from June 17-20, 2015, at Université Paris Sud in Orsay, France. The Langlands correspondence (nowadays called the usual Langlands correspondence), conjectured by Robert Langlands in the late 1960s and early 1970s, has recently seen some new mysterious generalizations: the modular Langlands correspondence, the p-adic Langlands correspondence, and the geometric Langlands correspondence, the last of which seems to share deep connections with the Baum-Connes conjecture. The aim of this vo.
Author | : Edward Frenkel |
Publisher | : Cambridge University Press |
Total Pages | : 5 |
Release | : 2007-06-28 |
Genre | : Mathematics |
ISBN | : 0521854431 |
Download Langlands Correspondence for Loop Groups Book in PDF, Epub and Kindle
The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Author | : Colin J. Bushnell |
Publisher | : Springer Science & Business Media |
Total Pages | : 352 |
Release | : 2006-08-29 |
Genre | : Mathematics |
ISBN | : 354031511X |
Download The Local Langlands Conjecture for GL(2) Book in PDF, Epub and Kindle
The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.
Author | : Uwe Jannsen |
Publisher | : American Mathematical Soc. |
Total Pages | : 766 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 0821827979 |
Download Motives Book in PDF, Epub and Kindle
'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play the role of the missing rational cohomology. This work contains the texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991.
Author | : H. Jacquet |
Publisher | : Springer |
Total Pages | : 156 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540376127 |
Download Automorphic Forms on GL (2) Book in PDF, Epub and Kindle
Author | : Anne-Marie Aubert |
Publisher | : Springer |
Total Pages | : 289 |
Release | : 2019-04-16 |
Genre | : Mathematics |
ISBN | : 9811366284 |
Download Representations of Reductive p-adic Groups Book in PDF, Epub and Kindle
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 recent refinements, due to the author and her collaborators, and their current status. It also features an extensive account by Colin Bushnell of his work with Henniart on the fine structure of the local Langlands correspondence for general linear groups, beginning with a clear overview of Bushnell–Kutzko’s construction of cuspidal types for such groups. The remaining papers touch on a range of topics in this active area of modern mathematics: group actions on root data, explicit character formulas, classification of discrete series representations, unicity of types, local converse theorems, completions of Hecke algebras, p-adic symmetric spaces. All meet a high level of exposition. The book should be a valuable resource to graduate students and experienced researchers alike.
Author | : Colin J. Bushnell |
Publisher | : American Mathematical Soc. |
Total Pages | : 100 |
Release | : 2014-08-12 |
Genre | : Mathematics |
ISBN | : 082189417X |
Download To an Effective Local Langlands Correspondence Book in PDF, Epub and Kindle
Let F be a non-Archimedean local field. Let \mathcal{W}_{F} be the Weil group of F and \mathcal{P}_{F} the wild inertia subgroup of \mathcal{W}_{F}. Let \widehat {\mathcal{W}}_{F} be the set of equivalence classes of irreducible smooth representations of \mathcal{W}_{F}. Let \mathcal{A}^{0}_{n}(F) denote the set of equivalence classes of irreducible cuspidal representations of \mathrm{GL}_{n}(F) and set \widehat {\mathrm{GL}}_{F} = \bigcup _{n\ge 1} \mathcal{A}^{0}_{n}(F). If \sigma \in \widehat {\mathcal{W}}_{F}, let ^{L}{\sigma }\in \widehat {\mathrm{GL}}_{F} be the cuspidal representation matched with \sigma by the Langlands Correspondence. If \sigma is totally wildly ramified, in that its restriction to \mathcal{P}_{F} is irreducible, the authors treat ^{L}{\sigma} as known. From that starting point, the authors construct an explicit bijection \mathbb{N}:\widehat {\mathcal{W}}_{F} \to \widehat {\mathrm{GL}}_{F}, sending \sigma to ^{N}{\sigma}. The authors compare this "naïve correspondence" with the Langlands correspondence and so achieve an effective description of the latter, modulo the totally wildly ramified case. A key tool is a novel operation of "internal twisting" of a suitable representation \pi (of \mathcal{W}_{F} or \mathrm{GL}_{n}(F)) by tame characters of a tamely ramified field extension of F, canonically associated to \pi. The authors show this operation is preserved by the Langlands correspondence.
Author | : Christophe Breuil |
Publisher | : American Mathematical Soc. |
Total Pages | : 127 |
Release | : 2012-02-22 |
Genre | : Mathematics |
ISBN | : 0821852272 |
Download Towards a Modulo $p$ Langlands Correspondence for GL$_2$ Book in PDF, Epub and Kindle
The authors construct new families of smooth admissible $\overline{\mathbb{F}}_p$-representations of $\mathrm{GL}_2(F)$, where $F$ is a finite extension of $\mathbb{Q}_p$. When $F$ is unramified, these representations have the $\mathrm{GL}_2({\mathcal O}_F)$-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod $p$ Langlands correspondence.
Author | : Martin Luu |
Publisher | : American Mathematical Soc. |
Total Pages | : 116 |
Release | : 2015-10-27 |
Genre | : Mathematics |
ISBN | : 1470414228 |
Download Deformation Theory and Local-Global Compatibility of Langlands Correspondences Book in PDF, Epub and Kindle
The deformation theory of automorphic representations is used to study local properties of Galois representations associated to automorphic representations of general linear groups and symplectic groups. In some cases this allows to identify the local Galois representations with representations predicted by a local Langlands correspondence.