Modular Curves and Abelian Varieties J. Cremona

ISBN: 9783764365868

Published: February 23rd 2004

Hardcover

289 pages


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Modular Curves and Abelian Varieties  by  J. Cremona

Modular Curves and Abelian Varieties by J. Cremona
February 23rd 2004 | Hardcover | PDF, EPUB, FB2, DjVu, AUDIO, mp3, ZIP | 289 pages | ISBN: 9783764365868 | 8.66 Mb

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 theMoreIt 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 Fermats 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).



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