L-Functions and Galois Representations (London Mathematical Society Lecture Note Series, Series Number 320)

This Collection Of Survey And Research Articles Brings Together Topics At The Forefront Of The Theory Of L-functions And Galois Representations. Highlighting Important Progress In Areas Such As The Local Langlands Programme, Automorphic Forms And Selmer Groups, This Timely Volume Treats Some Of The Most Exciting Recent Developments In The Field. Included Are Survey Articles From Khare On Serre's Conjecture, Yafaev On The André-oort Conjecture, Emerton On His Theory Of Jacquet Functors, Venjakob On Non-commutative Iwasawa Theory And Vigneras On Mod P Representations Of Gl(2) Over P-adic Fields. There Are Also Research Articles By: Böckle, Buzzard, Cornut And Vatsal, Diamond, Hida, Kurihara And R. Pollack, Kisin, Nekovář, And Bertolini, Darmon And Dasgupta. Presenting The Very Latest Research On L-functions And Galois Representations, This Volume Is Indispensable For Researchers In Algebraic Number Theory. Stark-heegner Points And Special Values Of L-series / Massimo Bertolini, Henri Darmon, And Samit Dasgupta -- Presentations Of Universal Deformation Rings / Gebhard Böckle -- Eigenvarieties / Kevin Buzzard -- Nontriviality Of Rankin-selberg L-functions And Cm Points / Christophe Cornut And Vinayak Vatsal -- A Correspondence Between Representations Of Local Galois Groups And Lie-type Groups / Fred Diamond -- Non-vanishing Modulo P Of Hecke L-values And Application / Haruzo Hida -- Serre's Modularity Conjecture : A Survey Of The Level One Case / Chandrashekhar Khare -- Two P-adic L-functions And Rational Points On Elliptic Curves With Supersingular Reduction / Masato Kurihara And Robert Pollack -- From The Birch And Swinnerton-dyer Conjecture To Non-commutative Iwasawa Theory Via The Equivalent Tamagawa Number Conjecture : A Survey / Otmar Venjakob -- The André-oort Conjecture : A Survey / Andrei Yafaev -- Locally Analytic Representation Theory Of P-adic Reductive Groups : A Summary Of Some Recent Developments / Matthew Emerton -- Modularity For Some Geometric Galois Representations / Mark Kisin ; With An Appendix By Ofer Gabber -- The Euler System Method For Cm Points On Shimura Curves / Jan Nekovář -- Representations Irréductibles De Gl(2, F) Modulo P / Marie-france Vignéras. Edited By David Burns, Kevin Buzzard And Jan Nekovář. Includes Bibliographical References. Cover......Page 1 Title Page......Page 6 Copyright Page......Page 7 Contents......Page 8 Preface......Page 10 List of participants......Page 12 Stark-CHeegner points and special values of L-series......Page 14 Presentations of universal deformation rings......Page 37 Eigenvarieties......Page 72 Nontriviality of Rankin-Selberg L-functions and CM points......Page 134 A correspondence between representations of local Galois groups and Lie-type groups......Page 200 Non-vanishing modulo p of Hecke L ̈Cvalues and application......Page 220 Serre's modularity conjecture: a survey of the level one case......Page 283 Two p-adic L-functions and rational points on elliptic curves with supersingular reduction......Page 313 From the Birch and Swinnerton-Dyer Conjecture to non-commutative Iwasawa theory via the Equivariant Tamagawa Number Conjecture- a survey......Page 346 The Andre-Oort conjecture - a survey......Page 394 Locally analytic representation theory of p-adic reductive groups:a summary of some recent developments......Page 420 Modularity for some geometric Galois representations - with an appendix by Ofer Gabber......Page 451 The Euler system method for CM points on Shimura curves......Page 484 Representations irr??eductibles de GL(2, F) modulo p......Page 561 Cambridge University Press Cover 1 Title Page 6 Copyright Page 7 Contents 8 Preface 10 List of participants 12 Stark-CHeegner points and special values of L-series 14 Presentations of universal deformation rings 37 Eigenvarieties 72 Nontriviality of Rankin-Selberg L-functions and CM points 134 A correspondence between representations of local Galois groups and Lie-type groups 200 Non-vanishing modulo p of Hecke L ̈Cvalues and application 220 Serre's modularity conjecture: a survey of the level one case 283 Two p-adic L-functions and rational points on elliptic curves with supersingular reduction 313 From the Birch and Swinnerton-Dyer Conjecture to non-commutative Iwasawa theory via the Equivariant Tamagawa Number Conjecture- a survey 346 The Andre-Oort conjecture - a survey 394 Locally analytic representation theory of p-adic reductive groups:a summary of some recent developments 420 Modularity for some geometric Galois representations - with an appendix by Ofer Gabber 451 The Euler system method for CM points on Shimura curves 484 Representations irr??eductibles de GL(2, F) modulo p 561 0521694159,9780521694155,9780511721267,0511721269 Highlighting important progress being made in areas such as the local Langlands programme and automorphic forms, this timely volume is indispensable for researchers in the area of L-functions and Galois representations. Articles include Khare on Serre's conjecture, Yafaev on the André-Oort conjecture, and Emerton on Jacquet functors. Highlighting important progress being made in areas such as the local Langlands programme and automorphic forms, this timely volume is indispensable for researchers in the area of L-functions and Galois representations. Articles include Khare on Serre's conjecture, Yafaev on the Andre-Oort conjecture, and Emerton on Jacquet functors. Timely collection of articles bringing together topics at the forefront of the theory, including the local Langlands programme and automorphic forms