Elliptic curves with maximal Galois action on their torsion points

被引：22

作者：

Zywina, David ^{[1
]}

机构：

[1] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2010年 / 42卷

关键词：

EXCEPTIONAL PRIMES; THEOREM; FIELDS; NUMBER; SUMS;

D O I：

10.1112/blms/bdq039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation rho(E) : Gal((k) over bar/ k) -> GL(2)(Z). For a fixed number field k, we describe the image of rho(E) for a ` random' elliptic curve E over k. In particular, if k not equal Q is linearly disjoint from the cyclotomic extension of Q, then.E will be surjective for ` most' elliptic curves over k.

引用

页码：811 / 826

页数：16

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