Lower bounds for the canonical height on elliptic curves over abelian extensions
| dc.creator | Baker, Matthew | |
| dc.date | 2002-12-10 | |
| dc.date | 2002-12-16 | |
| dc.date.accessioned | 2026-07-07T04:53:39Z | |
| dc.date.available | 2026-07-07T04:53:39Z | |
| dc.description | Let K be a number field and let E/K be an elliptic curve. If E has complex multiplication, we show that there is a positive lower bound for the canonical height of non-torsion points on E defined over the maximal abelian extension K^ab of K. This is analogous to results of Amoroso-Dvornicich and Amoroso-Zannier for the multiplicative group. We also show that if E has non-integral j-invariant (so that in particular E does not have complex multiplication), then there exists C > 0 such that there are only finitely many points P in E(K^ab) of canonical height less than C. This strengthens a result of Hindry and Silverman. | |
| dc.description | 14 pages. Proof of Theorem 1.4 clarified | |
| dc.identifier | https://arxiv.org/abs/math/0212132 | |
| dc.identifier | http://arxiv.org/abs/math/0212132 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65938 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Lower bounds for the canonical height on elliptic curves over abelian extensions | |
| dc.type | text |