On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields

JOURNAL OF NUMBER THEORY

卷:128

Article

Vigni, Stefano

关键词: elliptic curves;    function fields;    Drinfeld-Heegner points;   

DOI  :  10.1016/j.jnt.2007.11.007

来源: Elsevier

【 摘 要 】

If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional chi-eigenspace (with chi a complex ring class character) provided that the projection onto this eigenspace of a suitable Drinfeld-Heegner point is non-zero. This represents the analogue in the function field setting of a theorem for elliptic curves over Q due to Bertolini and Darmon, and at the same time is a generalization of the main result proved by Brown in his monograph on Heegner modules. As in the number field case, our proof employs Kolyvagin-type arguments, and the cohomological machinery is started up by the control oil the Galois structure of the torsion of E provided by classical results of Igusa in positive characteristic. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free