Elliptic curves with maximal Galois action on their torsion points
Number Theory
2014-02-26 v1
Abstract
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(\bar{k}/k) \to GL_2(\hat{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\neq Q is linearly disjoint from the cyclotomic extension of Q, then \rho_E will be surjective for "most" elliptic curves over k.
Keywords
Cite
@article{arxiv.0809.3482,
title = {Elliptic curves with maximal Galois action on their torsion points},
author = {David Zywina},
journal= {arXiv preprint arXiv:0809.3482},
year = {2014}
}
Comments
14 pages