Elliptic curves and big Galois representations:
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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2008
|
| Schriftenreihe: | London Mathematical Society lecture note series
356 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (ix, 281 pages) |
| ISBN: | 9780511721281 |
| DOI: | 10.1017/CBO9780511721281 |
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| 520 | |a 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 | ||
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| author | Delbourgo, Daniel |
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| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511721281 |
| format | Electronic eBook |
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| isbn | 9780511721281 |
| language | English |
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| spelling | Delbourgo, Daniel Verfasser aut Elliptic curves and big Galois representations Daniel Delbourgo Elliptic Curves & Big Galois Representations Cambridge Cambridge University Press 2008 1 online resource (ix, 281 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 356 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Curves, Elliptic Galois theory Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Galois-Darstellung (DE-588)4221407-5 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Galois-Darstellung (DE-588)4221407-5 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-72866-9 https://doi.org/10.1017/CBO9780511721281 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Delbourgo, Daniel Elliptic curves and big Galois representations Curves, Elliptic Galois theory Elliptische Kurve (DE-588)4014487-2 gnd Galois-Darstellung (DE-588)4221407-5 gnd |
| subject_GND | (DE-588)4014487-2 (DE-588)4221407-5 |
| title | Elliptic curves and big Galois representations |
| title_alt | Elliptic Curves & Big Galois Representations |
| title_auth | Elliptic curves and big Galois representations |
| title_exact_search | Elliptic curves and big Galois representations |
| title_full | Elliptic curves and big Galois representations Daniel Delbourgo |
| title_fullStr | Elliptic curves and big Galois representations Daniel Delbourgo |
| title_full_unstemmed | Elliptic curves and big Galois representations Daniel Delbourgo |
| title_short | Elliptic curves and big Galois representations |
| title_sort | elliptic curves and big galois representations |
| topic | Curves, Elliptic Galois theory Elliptische Kurve (DE-588)4014487-2 gnd Galois-Darstellung (DE-588)4221407-5 gnd |
| topic_facet | Curves, Elliptic Galois theory Elliptische Kurve Galois-Darstellung |
| url | https://doi.org/10.1017/CBO9780511721281 |
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