Modular Curves And Abelian Varieties
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Author |
: John Cremona |
Publisher |
: Birkhäuser |
Total Pages |
: 291 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034879194 |
ISBN-13 |
: 3034879199 |
Rating |
: 4/5 (94 Downloads) |
Synopsis Modular Curves and Abelian Varieties by : John Cremona
This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matemtica (Bellaterra, Barcelona). The articles in this volume present the latest achievements in this extremely active field and will be of interest both to specialists and to students and researchers. Many contributions focus on generalizations of the Shimura-Taniyama conjecture to varieties such as elliptic Q-curves and Abelian varieties of GL_2-type. The book also includes several key articles in the subject that do not correspond to conference lectures.
Author |
: Vijaya Kumar Murty |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 128 |
Release |
: 1993 |
ISBN-10 |
: 9780821811795 |
ISBN-13 |
: 0821811797 |
Rating |
: 4/5 (95 Downloads) |
Synopsis Introduction to Abelian Varieties by : Vijaya Kumar Murty
This book presents an elementary and self-contained approach to Abelian varieties, a subject that plays a central role in algebraic and analytic geometry, number theory, and complex analysis. The book is based on notes from a course given at Concordia University and would be useful for independent study or as a textbook for graduate courses in complex analysis, Riemann surfaces, number theory, or analytic geometry. Murty works mostly over the complex numbers, discussing the theorem of Abel-Jacobi and Lefschetz's theorem on projective embeddings. After presenting some examples, Murty touches on Abelian varieties over number fields, as well as the conjecture of Tate (Faltings's theorem) and its relation to Mordell's conjecture. References are provided to guide the reader in further study.
Author |
: Allan Adler |
Publisher |
: Springer |
Total Pages |
: 205 |
Release |
: 2006-11-14 |
ISBN-10 |
: 9783540496090 |
ISBN-13 |
: 3540496092 |
Rating |
: 4/5 (90 Downloads) |
Synopsis Moduli of Abelian Varieties by : Allan Adler
This is a book aimed at researchers and advanced graduate students in algebraic geometry, interested in learning about a promising direction of research in algebraic geometry. It begins with a generalization of parts of Mumford's theory of the equations defining abelian varieties and moduli spaces. It shows through striking examples how one can use these apparently intractable systems of equations to obtain satisfying insights into the geometry and arithmetic of these varieties. It also introduces the reader to some aspects of the research of the first author into representation theory and invariant theory and their applications to these geometrical questions.
Author |
: Carel Faber |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 205 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783322901729 |
ISBN-13 |
: 3322901726 |
Rating |
: 4/5 (29 Downloads) |
Synopsis Moduli of Curves and Abelian Varieties by : Carel Faber
The Dutch Intercity Seminar on Moduli, which dates back to the early eighties, was an initiative of G. van der Geer, F. Oort and C. Peters. Through the years it became a focal point of Dutch mathematics and it gained some fame, also outside Holland, as an active biweekly research seminar. The tradition continues up to today. The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Hain, E. Looijenga, and F. Oort, originates from the seminar held in 1995--96. Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles.
Author |
: G Stevens |
Publisher |
: Springer Science & Business Media |
Total Pages |
: |
Release |
: 1988-01-01 |
ISBN-10 |
: 0817630481 |
ISBN-13 |
: 9780817630485 |
Rating |
: 4/5 (81 Downloads) |
Synopsis Arithmetic on Modular Curves by : G Stevens
Author |
: Fred Diamond |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 462 |
Release |
: 2006-03-30 |
ISBN-10 |
: 9780387272269 |
ISBN-13 |
: 0387272267 |
Rating |
: 4/5 (69 Downloads) |
Synopsis A First Course in Modular Forms by : Fred Diamond
This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.
Author |
: Seth Kleinerman |
Publisher |
: |
Total Pages |
: 46 |
Release |
: 2004 |
ISBN-10 |
: OCLC:77073330 |
ISBN-13 |
: |
Rating |
: 4/5 (30 Downloads) |
Synopsis On the Torsion Points of Elliptic Curves and Modular Abelian Varieties by : Seth Kleinerman
Author |
: Everett William Howe |
Publisher |
: |
Total Pages |
: 202 |
Release |
: 1993 |
ISBN-10 |
: UCAL:C3371759 |
ISBN-13 |
: |
Rating |
: 4/5 (59 Downloads) |
Synopsis Elliptic Curves and Ordinary Abelian Varieties Over Finite Fields by : Everett William Howe
Author |
: Jean-Pierre Serre |
Publisher |
: CRC Press |
Total Pages |
: 203 |
Release |
: 1997-11-15 |
ISBN-10 |
: 9781439863862 |
ISBN-13 |
: 1439863865 |
Rating |
: 4/5 (62 Downloads) |
Synopsis Abelian l-Adic Representations and Elliptic Curves by : Jean-Pierre Serre
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
Author |
: Haruzo Hida |
Publisher |
: World Scientific |
Total Pages |
: 468 |
Release |
: 2012 |
ISBN-10 |
: 9789814368643 |
ISBN-13 |
: 9814368644 |
Rating |
: 4/5 (43 Downloads) |
Synopsis Geometric Modular Forms and Elliptic Curves by : Haruzo Hida
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).