The rank of elliptic curves with rational 2-torsion points over large fields

被引：5

作者：

Im, BH ^{[1
]}

机构：

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 06期

关键词：

D O I：

10.1090/S0002-9939-05-08494-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let K be a number field, K an algebraic closure of K, G(K) the absolute Galois group Gal(<(K)overbar >/K), K-ab the maximal abelian extension of K and E/K an elliptic curve defined over K. In this paper, we prove that if all 2-torsion points of E/K are K-rational, then for each sigma epsilon G(K), E((K-ab)(sigma)) has infinite rank, and hence E( K s) has infinite rank.

引用

页码：1623 / 1630

页数：8