Torsion points on elliptic curves over function fields and a theorem of Igusa
| dc.creator | Bandini, A. | |
| dc.creator | Longhi, I. | |
| dc.creator | Vigni, S. | |
| dc.date | 2008-04-09 | |
| dc.date | 2008-05-30 | |
| dc.date.accessioned | 2026-07-07T09:48:19Z | |
| dc.date.available | 2026-07-07T09:48:19Z | |
| dc.description | If F is a global function field of characteristic p>3, we employ Tate's theory of analytic uniformization to give an alternative proof of a theorem of Igusa describing the image of the natural Galois representation on torsion points of non-isotrivial elliptic curves defined over F. Along the way, using basic properties of Faltings heights of elliptic curves, we offer a detailed proof of the function field analogue of a classical theorem of Shafarevich according to which there are only finitely many F-isomorphism classes of admissible elliptic curves defined over F with good reduction outside a fixed finite set of places of F. We end the paper with an application to torsion points rational over abelian extensions of F. | |
| dc.description | 28 pages, final version, few minor changes | |
| dc.identifier | https://arxiv.org/abs/0804.1425 | |
| dc.identifier | http://arxiv.org/abs/0804.1425 | |
| dc.identifier | doi:10.1016/j.exmath.2008.06.001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164170 | |
| dc.subject | Number Theory | |
| dc.subject | 11G05; 11F80 | |
| dc.title | Torsion points on elliptic curves over function fields and a theorem of Igusa | |
| dc.type | text |