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Modular Curves and Abelian Varieties

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 199/5 ( reviews)

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Book Synopsis Modular Curves and Abelian Varieties by : John Cremona

Download or read book Modular Curves and Abelian Varieties written by John Cremona. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Abelian Varieties

1993 Mathematics
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Release : 1993
Genre : Mathematics
Kind : eBook
Book Rating : 797/5 ( reviews)

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Book Synopsis Introduction to Abelian Varieties by : Vijaya Kumar Murty

Download or read book Introduction to Abelian Varieties written by Vijaya Kumar Murty. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Arithmetic on Modular Curves

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 652/5 ( reviews)

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Book Synopsis Arithmetic on Modular Curves by : G. Stevens

Download or read book Arithmetic on Modular Curves written by G. Stevens. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: One of the most intriguing problems of modern number theory is to relate the arithmetic of abelian varieties to the special values of associated L-functions. A very precise conjecture has been formulated for elliptic curves by Birc~ and Swinnerton-Dyer and generalized to abelian varieties by Tate. The numerical evidence is quite encouraging. A weakened form of the conjectures has been verified for CM elliptic curves by Coates and Wiles, and recently strengthened by K. Rubin. But a general proof of the conjectures seems still to be a long way off. A few years ago, B. Mazur [26] proved a weak analog of these c- jectures. Let N be prime, and be a weight two newform for r 0 (N) . For a primitive Dirichlet character X of conductor prime to N, let i\ f (X) denote the algebraic part of L (f , X, 1) (see below). Mazur showed in [ 26] that the residue class of Af (X) modulo the "Eisenstein" ideal gives information about the arithmetic of Xo (N). There are two aspects to his work: congruence formulae for the values Af(X) , and a descent argument. Mazur's congruence formulae were extended to r 1 (N), N prime, by S. Kamienny and the author [17], and in a paper which will appear shortly, Kamienny has generalized the descent argument to this case.

Moduli of Abelian Varieties

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 092/5 ( reviews)

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Book Synopsis Moduli of Abelian Varieties by : Allan Adler

Download or read book Moduli of Abelian Varieties written by Allan Adler. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Moduli of Curves and Abelian Varieties

2012-12-06 Technology & Engineering
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Release : 2012-12-06
Genre : Technology & Engineering
Kind : eBook
Book Rating : 726/5 ( reviews)

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Book Synopsis Moduli of Curves and Abelian Varieties by : Carel Faber

Download or read book Moduli of Curves and Abelian Varieties written by Carel Faber. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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