On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields
| Autor: | Vigni, S. |
|---|---|
| Rok vydání: | 2008 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jnt.2007.11.007 |
| Popis: | 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. Comment: 20 pages, to appear in J. Number Theory |
| Databáze: | arXiv |
| Externí odkaz: |
|