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

Im, Bo-Hae

Canadian journal of mathematics, Tome 58 (2006) no. 4, pp. 796-819

Résumé

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 $2P\ne O$ and $3P\ne O$ , then for each $\sigma \,\in \,\text{Gal(}\overline{K}/K\text{)}$ , the Mordell–Weil group $E({{\overline{K}}^{\sigma }})$ of $E$ over the fixed subfield of $\bar{K}$ under $\sigma $ has infinite rank.

Détail

DOI : 10.4153/CJM-2006-032-4

Mots-clés : 11G05

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