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Elliptic curves and big Galois representations /
"The mysterious properties of modular forms 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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2008.
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| Colección: | London Mathematical Society lecture note series ;
356. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | "The mysterious properties of modular forms 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. One can then establish finiteness results for big Selmer groups. Finally, at weight two, the arithmetic invariants of these Selmer groups allow the control of data from the BSD conjecture." "This is the first book on the subject, and the material is introduced from scratch; both graduate students and professional number theorists will find this an ideal introduction to the subject. Material at the very forefront of current research is included, and numerical examples encourage the reader to interpret abstract theorems in concrete cases."--Jacket |
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| Descripción Física: | 1 online resource (ix, 281 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 275-279) and index. |
| ISBN: | 9781107363069 1107363063 9780511894046 051189404X 9780511721281 0511721285 9781107367975 1107367972 |