Mordell-Weil groups and the rank of elliptic curves over large fields
| dc.creator | Im, Bo-Hae | |
| dc.date | 2004-11-24 | |
| dc.date | 2004-11-25 | |
| dc.date.accessioned | 2026-07-07T05:14:38Z | |
| dc.date.available | 2026-07-07T05:14:38Z | |
| dc.description | Let $K$ be a number field, $\bar{K}$ an algebraic closure of $K$ and $E/K$ an elliptic curve defined over $K$. In this paper, we prove that if $E/K$ has a $K$-rational point $P$ such that $2P\neq O$ and $3P\neq O$, then for each $σ\in Gal(\bar{K}/K)$, the Mordell-Weil group $E(\bar{K}^σ)$ of $E$ over the fixed subfield of $\bar{K}$ under $σ$ has infinite rank. | |
| dc.description | 30 pages. submitted, only change of the title | |
| dc.identifier | https://arxiv.org/abs/math/0411533 | |
| dc.identifier | http://arxiv.org/abs/math/0411533 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73353 | |
| dc.subject | Number Theory | |
| dc.subject | 11G05 | |
| dc.title | Mordell-Weil groups and the rank of elliptic curves over large fields | |
| dc.type | text |