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Elliptic Curves, Hilbert Modular Forms and Galois Deformations [electronic resource] /by Laurent Berger, Gebhard Böckle, Lassina Dembélé, Mladen Dimitrov, Tim Dokchitser, John Voight.

by Berger, Laurent [author.]; Böckle, Gebhard [author.]; Dembélé, Lassina [author.]; Dimitrov, Mladen [author.]; Dokchitser, Tim [author.]; Voight, John [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Advanced Courses in Mathematics - CRM Barcelona: Publisher: Basel : Springer Basel : 2013.Description: XII, 249 p. 11 illus., 2 illus. in color. online resource.ISBN: 9783034806183.Subject(s): Mathematics | Algebra | Geometry, algebraic | Number theory | Mathematics | Number Theory | Algebraic Geometry | AlgebraDDC classification: 512.7 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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