Towards a Modulo $p$ Langlands Correspondence for GL$_2$ PDF Download

Author: Christophe Breuil
Publisher: American Mathematical Soc.
ISBN: 0821852272
Category : Mathematics
Languages : en
Pages : 127

View

Book Description
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:
Publisher: World Scientific
ISBN:
Category :
Languages : en
Pages : 1191

View

Book Description

Author: Ina Kersten
Publisher: Universitätsverlag Göttingen
ISBN: 3940344966
Category : Algebraic number theory
Languages : en
Pages : 213

View

Book Description
4e de couverture : "These proceedings contain most of the contributions to the Göttingen-Jerusalem Conference 2008 on "Symmetries in Algebra and Number Theory" including three addresses given at the conference opening, and two contributions to the Satellite Conference "On the Legacy of Hermann Weyl". The contributions are survey articles or report on recent work by the authors, for exemple new results on the famous Leopoldt conjecture."

Author: H. Jacquet
Publisher: Springer
ISBN: 3540376127
Category : Mathematics
Languages : en
Pages : 156

View

Book Description

Author: David Jordan
Publisher: Cambridge University Press
ISBN: 1009103474
Category : Mathematics
Languages : en
Pages : 408

View

Book Description
Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.

Author: John Coates
Publisher: Cambridge University Press
ISBN: 1139505653
Category : Mathematics
Languages : en
Pages : 321

View

Book Description
This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.

Author: Rajendra Bhatia
Publisher: World Scientific
ISBN: 9814462934
Category : Mathematics
Languages : en
Pages : 4137

View

Book Description
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Author: Farrell Brumley
Publisher: American Mathematical Soc.
ISBN: 147043573X
Category : Algebraic number theory
Languages : en
Pages : 376

View

Book Description
This volume contains the proceedings of the international conference ``Around Langlands Correspondences'', held from June 17-20, 2015, at Universite 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 volume is to present, 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: Colin J. Bushnell
Publisher: Springer Science & Business Media
ISBN: 354031511X
Category : Mathematics
Languages : en
Pages : 352

View

Book Description
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: Alf J. van der Poorten
Publisher: Springer Science & Business Media
ISBN: 3540794557
Category : Computers
Languages : en
Pages : 463

View

Book Description
This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.