Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group
| dc.creator | Ingram, Patrick | |
| dc.date | 2008-11-19 | |
| dc.date | 2008-12-10 | |
| dc.date.accessioned | 2026-07-07T12:10:41Z | |
| dc.date.available | 2026-07-07T12:10:41Z | |
| dc.description | Let $E$ be an elliptic surface over the curve $C$, defined over a number field $k$, let $P$ be a section of $E$, and let $\ell$ be a rational prime. For any non-singular fibre $E_t$, we bound the number of points $Q$ on $E_t$ of (algebraic) degree at most $D$ over $k$, such that $\ell^n Q=P_t$, for some $n\geq 1$. The bound obtained depends only on $\ell$, the surface and section in question, $D$, and the degree $[k(t):k]$; that is, it is uniform across all fibres of bounded degree. In special cases, we obtain more specific, in some instances sharp, bounds. | |
| dc.description | Introduction re-written, and minor additions. The results of the paper are largely unchanged, with one small observation added | |
| dc.identifier | https://arxiv.org/abs/0811.3109 | |
| dc.identifier | http://arxiv.org/abs/0811.3109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210003 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G05; 14J27 | |
| dc.title | Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group | |
| dc.type | text |