Geometric Modular Forms and Elliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Modular Forms and Elliptic Curves write by Haruzo Hida. This book was released on 2012. Geometric Modular Forms and Elliptic Curves available in PDF, EPUB and Kindle. 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
Introduction to Elliptic Curves and Modular Forms
Introduction to Elliptic Curves and Modular Forms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Elliptic Curves and Modular Forms write by Neal I. Koblitz. This book was released on 2012-12-06. Introduction to Elliptic Curves and Modular Forms available in PDF, EPUB and Kindle. The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.
Geometric Modular Forms and Elliptic Curves
Geometric Modular Forms and Elliptic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Modular Forms and Elliptic Curves write by Haruzo Hida. This book was released on 2012. Geometric Modular Forms and Elliptic Curves available in PDF, EPUB and Kindle. This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura?Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction.In this new second edition, a detailed description of Barsotti?Tate groups (including formal Lie groups) is added to Chapter 1. As an application, a down-to-earth description of formal deformation theory of elliptic curves is incorporated at the end of Chapter 2 (in order to make the proof of regularity of the moduli of elliptic curve more conceptual), and in Chapter 4, though limited to ordinary cases, newly incorporated are Ribet's theorem of full image of modular p-adic Galois representation and its generalization to ?big? ?-adic Galois representations under mild assumptions (a new result of the author). Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian ?-varieties and ?-curves).
Elliptic Curves, Modular Forms, and Their L-functions
Elliptic Curves, Modular Forms, and Their L-functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Curves, Modular Forms, and Their L-functions write by Álvaro Lozano-Robledo. This book was released on 2011. Elliptic Curves, Modular Forms, and Their L-functions available in PDF, EPUB and Kindle. 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.
Elliptic Curves, Modular Forms & Fermat's Last Theorem
Elliptic Curves, Modular Forms & Fermat's Last Theorem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Curves, Modular Forms & Fermat's Last Theorem write by John Coates. This book was released on 1997. Elliptic Curves, Modular Forms & Fermat's Last Theorem available in PDF, EPUB and Kindle. These proceedings are based on a conference at the Chinese University of Hong Kong, held in response to Andrew Wile's conjecture that every elliptic curve over Q is modular. The survey article describing Wile's work is included as the first article in the present edition.
