L-Functions and Galois Representations

doi:10.1017/CBO9780511721267

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Edited by David Burns, King's College London, Kevin Buzzard, Imperial College of Science, Technology and Medicine, London, Jan Nekovář, Université de Paris VI (Pierre et Marie Curie)

Publisher:: Cambridge University Press
Online publication date:: April 2010
Print publication year:: 2007
Online ISBN:: 9780511721267
DOI:: https://doi.org/10.1017/CBO9780511721267

Subjects:: Mathematics (general), Mathematics, Number Theory
Series:: London Mathematical Society Lecture Note Series (320)

83.99 (GBP)

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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.

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L-Functions and Galois Representations

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-x

List of participants
pp xi-xii

Stark–Heegner points and special values of L-series
pp 1-23

Presentations of universal deformation rings
pp 24-58

Eigenvarieties
pp 59-120

Nontriviality of Rankin-Selberg L-functions and CM points
pp 121-186

A correspondence between representations of local Galois groups and Lie-type groups
pp 187-206

Non-vanishing modulo p of Hecke L–values and application
pp 207-269

Serre's modularity conjecture: a survey of the level one case
pp 270-299

Two p-adic L-functions and rational points on elliptic curves with supersingular reduction
pp 300-332

From the Birch and Swinnerton-Dyer Conjecture to non-commutative Iwasawa theory via the Equivariant Tamagawa Number Conjecture - a survey
pp 333-380

The André-Oort conjecture - a survey
pp 381-406

Locally analytic representation theory of p-adic reductive groups: a summary of some recent developments
pp 407-437

Modularity for some geometric Galois representations - with an appendix by Ofer Gabber
pp 438-470

The Euler system method for CM points on Shimura curves
pp 471-547

Représentations irréductibles de GL(2, F) modulo p
pp 548-563

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L-Functions and Galois Representations

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