Elliptic Curves, Hilbert Modular Forms and Galois - download pdf or read online

By Laurent Berger,Gebhard Böckle,Lassina Dembélé,Mladen Dimitrov,Tim Dokchitser,John Voight

The notes during this quantity correspond to complex classes held on the Centre de Recerca Matemàtica as a part of the examine application in mathematics Geometry within the 2009-2010 educational year.

The notes via Laurent Berger supply an advent to p-adic Galois representations and Fontaine earrings, that are specifically worthy for describing many neighborhood deformation earrings at p that come up obviously in Galois deformation theory.

The notes by way of Gebhard Böckle provide a entire direction on Galois deformation concept, ranging from the foundational result of Mazur and discussing intimately the idea of pseudo-representations and their deformations, neighborhood deformations at areas l ≠ p and native deformations at p that are flat. within the final section,the result of Böckle and Kisin on shows of world deformation earrings over neighborhood ones are discussed.

 The notes by way of Mladen Dimitrov current the fundamentals of the mathematics idea of Hilbert modular kinds and kinds, with an emphasis at the examine of the photographs of the hooked up Galois representations, on modularity lifting theorems over completely actual quantity fields, and at the cohomology of Hilbert modular kinds with imperative coefficients.

 The notes by means of Lassina Dembélé and John Voight describe tools for appearing particular computations in areas of Hilbert modular varieties. those equipment rely on the Jacquet-Langlands correspondence and on computations in areas of quaternionic modular varieties, either for the case of certain and indefinite quaternion algebras. a number of examples are given, and functions to modularity of Galois representations are discussed.

 The notes by means of Tim Dokchitser describe the evidence, received via the writer in a joint venture with Vladimir Dokchitser, of the parity conjecture for elliptic curves over quantity fields less than the idea of finiteness of the Tate-Shafarevich staff. The assertion of the Birch and Swinnerton-Dyer conjecture is incorporated, in addition to an in depth examine of neighborhood and worldwide root numbers of elliptic curves and their classification.

Show description

Read or Download Elliptic Curves, Hilbert Modular Forms and Galois Deformations (Advanced Courses in Mathematics - CRM Barcelona) PDF

Similar number theory books

Download e-book for kindle: Birational Geometry, Rational Curves, and Arithmetic (Simons by Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel

​​​​This publication positive aspects contemporary advancements in a swiftly starting to be quarter on the interface of higher-dimensional birational geometry and mathematics geometry.  It makes a speciality of the geometry of areas of rational curves, with an emphasis on functions to mathematics questions.  Classically, mathematics is the learn of rational or necessary ideas of diophantine equations and geometry is the research of strains and conics.

Get Analytic Number Theory, Approximation Theory, and Special PDF

This ebook, in honor of Hari M. Srivastava, discusses crucial advancements in mathematical examine in a number of difficulties. It comprises thirty-five articles, written through eminent scientists from the overseas mathematical neighborhood, together with either study and survey works. matters coated comprise analytic quantity concept, combinatorics, targeted sequences of numbers and polynomials, analytic inequalities and functions, approximation of services and quadratures, orthogonality and particular and complicated services.

New PDF release: L-Functions and Arithmetic (London Mathematical Society

This quantity is an outgrowth of the LMS Durham Symposium on L-functions, held in July 1989. The symposium consisted of a number of brief classes, aimed toward featuring rigorous yet non-technical expositions of the most recent learn components, and a couple of person lectures on particular themes. The participants are all striking figures within the region of algebraic quantity idea and this quantity can be of lasting price to scholars and researchers operating within the region.

Download e-book for kindle: Quadratic Residues and Non-Residues: Selected Topics by Steve Wright

This e-book bargains an account of the classical idea of quadratic residues and non-residues with the aim of utilizing that concept as a lens wherein to view the advance of a few of the elemental tools hired in glossy easy, algebraic, and analytic quantity thought. the 1st 3 chapters current a few uncomplicated proof and the heritage of quadratic residues and non-residues and talk about numerous proofs of the legislations of Quadratic Reciprosity intensive, with an emphasis at the six proofs that Gauss released.

Additional resources for Elliptic Curves, Hilbert Modular Forms and Galois Deformations (Advanced Courses in Mathematics - CRM Barcelona)

Sample text

Download PDF sample

Elliptic Curves, Hilbert Modular Forms and Galois Deformations (Advanced Courses in Mathematics - CRM Barcelona) by Laurent Berger,Gebhard Böckle,Lassina Dembélé,Mladen Dimitrov,Tim Dokchitser,John Voight

by David

Rated 4.56 of 5 – based on 44 votes