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Elliptic Curves and Big Galois Representations.
・ISBN 978-0-521-72866-9 paper GB£ 85.00
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-0-511-72128-1
| 著者・編者 | Delbourgo, Daniel, |
|---|---|
| シリーズ | London Mathematical Society Lecture Note Series |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2008 |
| ページ数 | 288 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-2144＞ |
解説
The arithmetic properties of modular forms and elliptic curves lie at the heart of modern number theory. This book develops a generalisation of the method of Euler systems to a two-variable deformation ring. The resulting theory is then used to study the arithmetic of elliptic curves, in particular the Birch and Swinnerton-Dyer (BSD) formula. Three main steps are outlined: the first is to parametrise 'big' cohomology groups using (deformations of) modular symbols. Finiteness results for big Selmer groups are then established. Finally, at weight two, the arithmetic invariants of these Selmer groups allow the control of data from the BSD conjecture. As the first book on the subject, the material is introduced from scratch; both graduate students and professional number theorists will find this an ideal introduction. Material at the very forefront of current research is included, and numerical examples encourage the reader to interpret abstract theorems in concrete cases.