Small Heights in Large Non-Abelian Extensions
Number Theory
2018-10-24 v1
Abstract
Let E be an elliptic curve over the rationals. Let L be an infinite Galois extension of the rationals with uniformly bounded local degrees at almost all primes. We will consider the infinite extension L(E_tor) of the rationals where we adjoin all coordinates of torsion points of E. In this paper we will prove an effective lower bound for the height of non-zero elements in L(E_tor) that are not a root of unity.
Cite
@article{arxiv.1810.09669,
title = {Small Heights in Large Non-Abelian Extensions},
author = {Linda Frey},
journal= {arXiv preprint arXiv:1810.09669},
year = {2018}
}
Comments
29 pages, Comments welcome