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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. doi:10.1016/j.jnt.2012.05.020 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 | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Number Theory | ||||
Publisher: | Elsevier Science BV | ||||
ISSN: | 0022-314X | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol.132 | ||||
Number: | No.11 | ||||
Page Range: | pp. 2610-2629 | ||||
DOI: | 10.1016/j.jnt.2012.05.020 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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