On the pre-image of a point under an isogeny
| dc.creator | Reynolds, Jonathan | |
| dc.date | 2008-10-01 | |
| dc.date.accessioned | 2026-07-07T10:06:37Z | |
| dc.date.available | 2026-07-07T10:06:37Z | |
| dc.description | Given a rational point on a curve in a rational isogeny class, a natural question concerns the field of definition of its pre-images. The multiplication by m endomorphism is a powerful and much-used tool. The pre-images for this map are found by factorizing a monic polynomial of degree m^2. For m = 2, Everest and King gave examples where the existence of a quadratic factor coincided with the existence of a rational pre-image via a 2-isogeny. Nelson Stephens asked if this always happens and the question is answered in the affirmative. It is also shown that the analogue for m = 3 can only be false when there exists a rational point of order three and a small number of counterexamples are found. The results are proven over any field with characteristic not two or three. | |
| dc.description | 4 pages, submitted | |
| dc.identifier | https://arxiv.org/abs/0810.0092 | |
| dc.identifier | http://arxiv.org/abs/0810.0092 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170388 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G05; 11A41 | |
| dc.title | On the pre-image of a point under an isogeny | |
| dc.type | text |