On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields
| dc.creator | Vigni, S. | |
| dc.date | 2008-04-10 | |
| dc.date.accessioned | 2026-07-07T09:31:32Z | |
| dc.date.available | 2026-07-07T09:31:32Z | |
| dc.description | 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 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.description | 20 pages, to appear in J. Number Theory | |
| dc.identifier | https://arxiv.org/abs/0804.1658 | |
| dc.identifier | http://arxiv.org/abs/0804.1658 | |
| dc.identifier | doi:10.1016/j.jnt.2007.11.007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158493 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G05; 14G10 | |
| dc.title | On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields | |
| dc.type | text |