On the number of Mordell–Weil generators for cubic surfaces
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 0022-314XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.jnt.2012.05.020
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|
|Page Range:||pp. 2610-2629|
|Access rights to Published version:||Restricted or Subscription Access|
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