{"product_id":"elliptic-curves-hilbert-modular-forms-and-galois-deformations-paperback","title":"Elliptic Curves, Hilbert Modular Forms and Galois Deformations - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eLaurent Berger\u003c\/b\u003e (Author), \u003cb\u003eGebhard Böckle\u003c\/b\u003e (Author), \u003cb\u003eLassina Dembélé\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe notes in this volume correspond to advanced courses held at the Centre de Recerca Matem tica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe notes by Laurent Berger provide an introduction to \u003ci\u003ep\u003c\/i\u003e-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at \u003ci\u003ep\u003c\/i\u003e that arise naturally in Galois deformation theory.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe notes by Gebhard B ckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l p and local deformations at \u003ci\u003ep\u003c\/i\u003e which are flat. In the last section, the results of B ckle and Kisin on presentations of global deformation rings over local ones are discussed.\u003c\/p\u003e\u003cp\u003e The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients.\u003c\/p\u003e\u003cp\u003e The notes by Lassina Demb l  and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed.\u003c\/p\u003e\u003cp\u003e The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe notes by Laurent Berger provide an introduction to \u003ci\u003ep\u003c\/i\u003e-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at \u003ci\u003ep\u003c\/i\u003e that arise naturally in Galois deformation theory.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe notes by Gebhard Böckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l p and local deformations at \u003ci\u003ep\u003c\/i\u003e which are flat. In the last section, the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients.\u003c\/p\u003e\u003cp\u003e The notes by Lassina Dembélé and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed.\u003c\/p\u003e\u003cp\u003e The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 249\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.43 x 9.52 x 6.65 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e July 04, 2013\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704856146227,"sku":"9783034806176","price":71.78,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/dFpNdUFZc0JYRHNjZmQyNkxraGFwUT09.webp?v=1763366278","url":"https:\/\/www.vysn.com\/en-ca\/products\/elliptic-curves-hilbert-modular-forms-and-galois-deformations-paperback","provider":"VYSN","version":"1.0","type":"link"}