Realizing Rational Representations in Mordell-Weil Groups
Number Theory
2010-02-10 v2 Group Theory
Abstract
Let G be a finite group and V a finite-dimensional rational G-representation. We ask whether there exists a finite Galois extension L/K of number fields with Galois group G, an elliptic curve E/K, and a G-submodule of E(L) tensor Q isomorphic to V.
Cite
@article{arxiv.math/0401209,
title = {Realizing Rational Representations in Mordell-Weil Groups},
author = {Bo-Hae Im and Michael Larsen},
journal= {arXiv preprint arXiv:math/0401209},
year = {2010}
}
Comments
This is a major revision, with a new coauthor and a changed title. The part of the paper dealing with integral structures had a gap, so it has been removed. The rational part has been extended. A new section, using Heegner point methods, has been added. Formerly 9 pages, now 8 pages