Abelian l-Adic Representations 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 Abelian l-Adic Representations and Elliptic Curves write by Jean-Pierre Serre. This book was released on 1997-11-15. Abelian l-Adic Representations and Elliptic Curves available in PDF, EPUB and Kindle. 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
Topics in Galois Theory
Topics in Galois Theory - 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 Topics in Galois Theory write by Jean-Pierre Serre. This book was released on 2016-04-19. Topics in Galois Theory available in PDF, EPUB and Kindle. This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi
Rational Points on Modular Elliptic Curves
Rational Points on Modular 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 Rational Points on Modular Elliptic Curves write by Henri Darmon. This book was released on 2004. Rational Points on Modular Elliptic Curves available in PDF, EPUB and Kindle. The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
p-adic Differential Equations
p-adic Differential Equations - 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 p-adic Differential Equations write by Kiran S. Kedlaya. This book was released on 2010-06-10. p-adic Differential Equations available in PDF, EPUB and Kindle. Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
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. 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
