Mordell-Weil groups and the rank of elliptic curves over large fields

Details Mordell-Weil groups and the rank of elliptic curves over large fields Mordell-Weil groups and the rank of elliptic curves over large fields

2004-11-24

arxiv.org/abs/math/0411533v2

Mathematics

Number Theory

30 pages. submitted, only change of the title

Scientific paper

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
$\sigma\in Gal(\bar{K}/K)$, the Mordell-Weil group $E(\bar{K}^{\sigma})$ of $E$
over the fixed subfield of $\bar{K}$ under $\sigma$ has infinite rank.

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