L-Functions and Galois Representations

by Edited by David Burns , Kevin Buzzard , Jan Nekovář

• ISBN13: 9780521694155
• ISBN10: 0521694159
• Edition: 1st
• Format: Paperback
• Copyright: 2008-01-07
• Publisher: Cambridge University Press

Summary

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 Andrè-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, Nekovàr, 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

Preface	p. ix
List of participants	p. xi
Stark-Heegner points and special values of L-series	p. 1
Presentations of universal deformation rings	p. 24
Eigenvarieties	p. 59
Nontriviality of Rankin-Selberg L-functions and CM points	p. 121
A correspondence between representations of local Galois groups and Lie-type groups	p. 187
Non-vanishing modulo p of Hecke L-values and application	p. 207
Serre's modularity conjecture: a survey of the level one case	p. 270
Two p-adic L-functions and rational points on elliptic curves with supersingular reduction	p. 300
From the Birch and Swinnerton-Dyer Conjecture to non-commutative Iwasawa theory via the Equivariant Tamagawa Number Conjecture - a survey	p. 333
The Andre-Oort conjecture - a survey	p. 381
Locally analytic representation theory of p-adic reductive groups: a summary of some recent developments	p. 407
Modularity for some geometric Galois representations - with an appendix by Ofer Gabber	p. 438
The Euler system method for CM points on Shimura curves	p. 471
Representations irreductibles de GL(2, F) modulo p	p. 548
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