Elliptic Curves, Hilbert Modular Forms and Galois Deformations
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.
The book contains the first published notes on the recent developments and major changes in Galois deformation theory during the last decade (deformations of pseudo-representations, framed deformations, groupoids, etc.)A survey on the parity conjecture is presentedComputational aspects of Hilbert modular forms are presented by the people responsible for the most powerful and widely spread algorithms available