Elliptic Curves, Hilbert Modular Forms and Galois Deformations

by Laurent Berger, Gebhard Bockle, Lassina Dembele, Mladen Dimitrov, Tim Dokchitser, John Voight, Henri Darmon (Adapted by), Fred Diamond (Adapted by), Luis V. Dieulefait (Adapted by), Bas Edixhoven (Adapted by), Victor Rotger (Adapted by)

Overview

The notes in this volume correspond to advanced courses given at the Centre de Recerca Matemàtica (Bellaterra, Barcelona, Spain) as part of the Research Programme in Arithmetic Geometry in the 2009-2010 academic year. They are now available in printed form due to the many requests received by the organizers to make the content of the courses publicly available. The material covers the theory of p-adic Galois representations and Fontaine rings, Galois deformation theory, arithmetic and computational aspects of Hilbert modular forms, and the parity conjecture for elliptic curves.​

Product Details

ISBN-13:	9783034806176
Publisher:	Springer Basel
Publication date:	07/04/2013
Series:	Advanced Courses in Mathematics - CRM Barcelona Series
Edition description:	2013
Pages:	249
Product dimensions:	6.61(w) x 9.45(h) x 0.02(d)

Table of Contents

Part I: Galois Deformations.- On p-adic Galois Representations.- Deformations of Galois Representations.- Part II: Hilbert Modular Forms.- Arithmetic Aspects of Hilbert Modular Forms and Varieties.- Explicit Methods for Hilbert Modular Forms.- Part III: Elliptic Curves.- Notes on the Parity Conjecture.​