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 Andre-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: Boeckle, Buzzard, Cornut and Vatsal, Diamond, Hida, Kurihara and R. Pollack, Kisin, Nekovar, 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.
David Burns is a Professor in the Department of Mathematics at King's College, London. Kevin Buzzard is Professor of Pure Mathematics at the Imperial College, London. Jan Nekovar is a Professor in the Faculte de Mathematiques at the Universite de Paris VI (Pierre et Marie Curie).
Preface; List of participants; 1. Stark-Heegner points and special values of L-series Massimo Bertolini, Henri Darmon and Samit Dasgupta; 2. Presentations of universal deformation rings Gebhard Boeckle; Eigenvarieties Kevin Buzzard; 3. Nontriviality of Rankin-Selberg L-functions and CM points Christophe Cornut and Vinayak Vatsal; 4. A correspondence between representations of local Galois groups and Lie-type groups Fred Diamond; 5. Non-vanishing modulo p of Hecke L-values and application Haruzo Hida; 6. Serre's modularity conjecture: a survey of the level one case Chandrashekhar Khare; 7. Two p-adic L-functions and rational points on elliptic curves with supersingular reduction Masato Kurihara and Robert Pollack; 8. From the Birch and Swinnerton-Dyer Conjecture to non-commutative Iwasawa theory via the Equivariant Tamagawa Number Conjecture - a survey Otmar Venjakob; 9. The Andre-Oort conjecture - a survey Andrei Yafaev; 10. Locally analytic representation theory of p-adic reductive groups: a summary of some recent developments Matthew Emerton; 11. Modularity for some geometric Galois representations - with an appendix by Ofer Gabber Mark Kisin; 12. The Euler system method for CM points on Shimura curves Jan Nekovar; 13. Representations irreductibles de GL(2,F ) modulo p Marie-France Vigneras.