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Mordell--Weil Groups and the Rank of Elliptic Curves over Large Fields

Open Access article
 Printed: Aug 2006
  • Bo-Hae Im
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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 show english descriptions Elliptic curves over global fields [See also 14H52] 11G05 - Elliptic curves over global fields [See also 14H52]

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