An explicit open image theorem for products of elliptic curves

JOURNAL OF NUMBER THEORY

卷:168

Article

Lombardo, Davide¹ 

[1] Dept Math Orsay, Orsay, France

关键词: Elliptic curves;    Galois representations;    Open image theorem;   

DOI  :  10.1016/j.jnt.2016.04.017

来源: Elsevier

【 摘 要 】

Let K be a number field and let E-1, ..., E-n be elliptic curves over K, pairwise non-isogenous over (K) over bar and without complex multiplication over (K) over bar. We study the image G(infinity) of the adelic representation of Gal ((K) over bar /K) naturally attached to E-1 x ... x E-n. The main result is an explicit bound for the index of G(infinity) in {(x(1), ..., x(m)) is an element of GL(2) (Z)(n) vertical bar det x(i) = det x(j) for all i, j}. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free