The arithmetic of QM-abelian surfaces through their Galois representations

摘要

This note provides an insight to the diophantine properties of abelian surfaces with quaternionic multiplication over number fields. We study the fields of definition of the endomorphisms on these abelian varieties and the images of the Galois representations on their Tate modules. We illustrate our results with an explicit example. (C) 2004 Elsevier Inc. All rights reserved.