Automorphic Forms and Galois Representations: Volume 1

Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.

Fred Diamond (Edited by), Payman L. Kassaei (Edited by), Minhyong Kim (Edited by)

9781107691926, Cambridge University Press

Paperback / softback, published 16 October 2014

386 pages
22.6 x 15.2 x 2 cm, 0.52 kg

Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume one include the Shafarevich Conjecture, effective local Langlands correspondence, p-adic L-functions, the fundamental lemma, and other topics of contemporary interest.

Preface
List of contributors
1. A semi-stable case of the Shafarevich conjecture V. Abrashkin
2. Irreducible modular representations of the Borel subgroup of GL2(Qp) L. Berger and M. Vienney
3. p-adic L-functions and Euler systems: a tale in two trilogies M. Bertolini, F. Castella, H. Darmon, S. Dasgupta, K. Prasanna and V. Rotger
4. Effective local Langlands correspondence C. J. Bushnell
5. The conjectural connections between automorphic representations and Galois representations K. Buzzard and T. Gee
6. Geometry of the fundamental lemma P.-H. Chaudouard
7. The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings G. Chenevier
8. La série principale unitaire de GL2(Qp): vecteurs localement analytiques P. Colmez
9. Equations différentielles p-adiques et modules de Jacquet analytiques G. Dospinescu.

Subject Areas: Topology [PBP], Geometry [PBM], Number theory [PBH], Mathematics [PB]