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On the number of Mordell–Weil generators for cubic surfaces
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Siksek, Samir. (2012) On the number of Mordell–Weil generators for cubic surfaces. Journal of Number Theory, Vol.132 (No.11). pp. 2610-2629. ISSN 0022-314X
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Official URL: http://dx.doi.org/10.1016/j.jnt.2012.05.020
Abstract
Let S be a smooth cubic surface over a field K. It is well-known that new K-rational points may be obtained from old ones by secant and tangent constructions. In this paper we prove, for a cubic surface containing a pair of skew rational lines over a field with at least 13 elements, that the rational points are generated by just one point. We also prove a cubic surface analogue of the unboundedness of ranks conjecture for elliptic curves over the rationals.
| Item Type: | Journal Article |
|---|---|
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Journal of Number Theory |
| Publisher: | Elsevier Science BV |
| ISSN: | 0022-314X |
| Date: | 2012 |
| Volume: | Vol.132 |
| Number: | No.11 |
| Page Range: | pp. 2610-2629 |
| Identification Number: | 10.1016/j.jnt.2012.05.020 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/49720 |
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