Abelian L Adic Representations And Elliptic Curves
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Abelian L Adic Representations And Elliptic Curves
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Author : Jean-Pierre Serre
language : en
Publisher: CRC Press
Release Date : 1997-11-15
Abelian L Adic Representations And Elliptic Curves written by Jean-Pierre Serre and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-15 with Mathematics categories.
This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Abelian L Adic Representations And Elliptic Curves
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Author : Jean Pierre Serre
language : en
Publisher:
Release Date : 1968
Abelian L Adic Representations And Elliptic Curves written by Jean Pierre Serre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Abelian P Adic Representations And Elliptic Curves
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Author : Jean-Pierre Serre
language : en
Publisher:
Release Date : 1968
Abelian P Adic Representations And Elliptic Curves written by Jean-Pierre Serre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Abelian Adic Representations And Elliptic Curves
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Author : Jean-Pierre Serre
language : en
Publisher:
Release Date : 1968
Abelian Adic Representations And Elliptic Curves written by Jean-Pierre Serre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Abelian One Adic Representations And Elliptic Curves
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Author : Jean Pierre Serre
language : en
Publisher:
Release Date : 1968
Abelian One Adic Representations And Elliptic Curves written by Jean Pierre Serre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Abelian groups categories.
Geometric Modular Forms And Elliptic Curves
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Author : Haruzo Hida
language : en
Publisher: World Scientific
Release Date : 2012
Geometric Modular Forms And Elliptic Curves written by Haruzo Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
1. An algebro-geometric tool box. 1.1. Sheaves. 1.2. Schemes. 1.3. Projective schemes. 1.4. Categories and functors. 1.5. Applications of the key-lemma. 1.6. Group schemes. 1.7. Cartier duality. 1.8. Quotients by a group scheme. 1.9. Morphisms. 1.10. Cohomology of coherent sheaves. 1.11. Descent. 1.12. Barsotti-Tate groups. 1.13. Formal scheme -- 2. Elliptic curves. 2.1. Curves and divisors. 2.2. Elliptic curves. 2.3. Geometric modular forms of level 1. 2.4. Elliptic curves over C. 2.5. Elliptic curves over p-adic fields. 2.6. Level structures. 2.7. L-functions of elliptic curves. 2.8. Regularity. 2.9. p-ordinary moduli problems. 2.10. Deformation of elliptic curves -- 3. Geometric modular forms. 3.1. Integrality. 3.2. Vertical control theorem. 3.3. Action of GL(2) on modular forms -- 4. Jacobians and Galois representations. 4.1. Jacobians of stable curves. 4.2. Modular Galois representations. 4.3. Fullness of big Galois representations -- 5. Modularity problems. 5.1. Induced and extended Galois representations. 5.2. Some other solutions. 5.3. Modularity of Abelian Q-varieties
Abelian L Adic Representations And Alliptic Curves
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Author : Jean-Pierre Serre
language : en
Publisher:
Release Date : 1968
Abelian L Adic Representations And Alliptic Curves written by Jean-Pierre Serre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Elliptic Curves Hilbert Modular Forms And Galois Deformations
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Author : Laurent Berger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-13
Elliptic Curves Hilbert Modular Forms And Galois Deformations written by Laurent Berger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-13 with Mathematics categories.
The 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. The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory. The 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 p which are flat. In the last section,the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed. 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. 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. 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.
Elliptic Curves Modular Forms And Their L Functions
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Author : Álvaro Lozano-Robledo
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Elliptic Curves Modular Forms And Their L Functions written by Álvaro Lozano-Robledo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular forms, and $L$-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.
Arithmetic Theory Of Elliptic Curves
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Author : J. Coates
language : en
Publisher: Springer
Release Date : 2006-11-14
Arithmetic Theory Of Elliptic Curves written by J. Coates and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.