Vanishing of some Galois cohomology groups for elliptic curves
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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Book Section |
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Springer
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40708/ |
| _version_ | 1848796121660391424 |
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| author | Lawson, Tyler Wuthrich, Christian |
| author2 | Loeffler, David |
| author_facet | Loeffler, David Lawson, Tyler Wuthrich, Christian |
| author_sort | Lawson, Tyler |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:42:57Z |
| format | Book Section |
| id | nottingham-40708 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:42:57Z |
| publishDate | 2016 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-407082020-05-04T20:05:24Z https://eprints.nottingham.ac.uk/40708/ Vanishing of some Galois cohomology groups for elliptic curves Lawson, Tyler Wuthrich, Christian 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. Springer Loeffler, David Zerbes, Sarah Livia 2016 Book Section PeerReviewed Lawson, Tyler and Wuthrich, Christian (2016) Vanishing of some Galois cohomology groups for elliptic curves. In: Elliptic curves, modular forms and Iwasawa theory: in honour of John H. Coates' 70th birthday, Cambridge, UK, March 2015. Springer proceedings in mathematics & statistics (188). Springer, pp. 373-399. ISBN 978-3-319-45032-2 |
| spellingShingle | Lawson, Tyler Wuthrich, Christian Vanishing of some Galois cohomology groups for elliptic curves |
| title | Vanishing of some Galois cohomology groups for elliptic curves |
| title_full | Vanishing of some Galois cohomology groups for elliptic curves |
| title_fullStr | Vanishing of some Galois cohomology groups for elliptic curves |
| title_full_unstemmed | Vanishing of some Galois cohomology groups for elliptic curves |
| title_short | Vanishing of some Galois cohomology groups for elliptic curves |
| title_sort | vanishing of some galois cohomology groups for elliptic curves |
| url | https://eprints.nottingham.ac.uk/40708/ |