Abstract
Let E/Q be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of Q obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group H1(G, E[p]) does not vanish, and investigate the analogous question for E[pi ] when i > 1. We include an application to the verification of certain cases of the Birch and Swinnerton-Dyer conjecture, and another application to the Grunwald–Wang problem for elliptic curves.
| Original language | English (US) |
|---|---|
| Title of host publication | Elliptic Curves, Modular Forms and Iwasawa Theory |
| Editors | David Loeffler, Sarah Livia Zerbes |
| Publisher | Springer New York LLC |
| Pages | 373-399 |
| Number of pages | 27 |
| ISBN (Print) | 9783319450315 |
| DOIs | |
| State | Published - 2016 |
| Event | Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 - Cambridge, United Kingdom Duration: Mar 25 2015 → Mar 27 2015 |
Publication series
| Name | Springer Proceedings in Mathematics and Statistics |
|---|---|
| Volume | 188 |
| ISSN (Print) | 2194-1009 |
| ISSN (Electronic) | 2194-1017 |
Other
| Other | Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 |
|---|---|
| Country/Territory | United Kingdom |
| City | Cambridge |
| Period | 3/25/15 → 3/27/15 |
Bibliographical note
Funding Information:Tyler Lawson’s work is partially supported by NSF DMS-1206008.
Publisher Copyright:
© Springer International Publishing Switzerland 2016
Keywords
- Birch and Swinnerton-Dyer conjecture
- Elliptic curves
- Galois cohomology
- Grunwald-Wang problem