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

dc.creatorVigni, S.
dc.date2008-04-10
dc.date.accessioned2026-07-07T09:31:32Z
dc.date.available2026-07-07T09:31:32Z
dc.descriptionIf 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 eigenspace relative to a fixed complex ring class character provided that the projection onto this eigenspace of a suitable Drinfeld-Heegner point is nonzero. This represents the analogue in the function field setting of a theorem for rational elliptic curves 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 on the Galois structure of the torsion of E provided by classical results of Igusa in positive characteristic.
dc.description20 pages, to appear in J. Number Theory
dc.identifierhttps://arxiv.org/abs/0804.1658
dc.identifierhttp://arxiv.org/abs/0804.1658
dc.identifierdoi:10.1016/j.jnt.2007.11.007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158493
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11G05; 14G10
dc.titleOn ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields
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