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Mordell--Weil Groups and the Rank of Elliptic Curves over Large Fields |
Canad. J. Math. 58(2006), 796-819
Published:2006-08-01
Printed: Aug 2006
Printed: Aug 2006
- Bo-Hae Im
Abstract
Let $K$ be a number field, $\overline{K}$ 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 $\sigma\in \Gal(\overline{K}/K)$, the Mordell--Weil group
$E(\overline{K}^{\sigma})$ of $E$ over the fixed subfield of
$\overline{K}$ under $\sigma$ has infinite rank.
| MSC Classifications: | 11G05 - Elliptic curves over global fields [See also 14H52] |