Realizing Rational Representations in Mordell-Weil Groups

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.

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