| Modular Curves and Abelian Varieties 2004 Edition Contributor(s): Cremona, John (Editor), Lario, Joan-Carles (Editor), Quer, Jordi (Editor) |
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ISBN: 3764365862 ISBN-13: 9783764365868 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: February 2004 Annotation: This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matem?tica (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. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | Geometry - Algebraic |
| Dewey: 512.7 |
| LCCN: 2004041077 |
| Series: Progress in Mathematics |
| Physical Information: 0.69" H x 6.14" W x 9.21" (1.33 lbs) 289 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: It would be difficult to overestimate the influence and importance of modular forms, modular curves, and modular abelian varieties in the development of num- ber theory and arithmetic geometry during the last fifty years. These subjects lie at the heart of many past achievements and future challenges. For example, the theory of complex multiplication, the classification of rational torsion on el- liptic curves, the proof of Fermat's Last Theorem, and many results towards the Birch and Swinnerton-Dyer conjecture all make crucial use of modular forms and modular curves. A conference was held from July 15 to 18, 2002, at the Centre de Recerca Matematica (Bellaterra, Barcelona) under the title "Modular Curves and Abelian Varieties". Our conference presented some of the latest achievements in the theory to a diverse audience that included both specialists and young researchers. We emphasized especially the conjectural generalization of the Shimura-Taniyama conjecture to elliptic curves over number fields other than the field of rational numbers (elliptic Q-curves) and abelian varieties of dimension larger than one (abelian varieties of GL2-type). |