L-Functions and Galois Representations

✍ Scribed by David Burns, Kevin Buzzard, Jan Nekovár

• Publisher: Cambridge University Press
• Year: 2008
• Tongue: English
• Leaves: 576
• Series: London Mathematical Society Lecture Note Series
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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