International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 52, Pages 2795-2808
doi:10.1155/S0161171204302243
The field of moduli of quaternionic multiplication on abelian varieties
Departament de Matemàtica Aplicada IV (EPSEVG), Universitat Politècnica de Catalunya, Av. Victor Balaguer s/n, Vilanova i la Geltrú, 08800, Spain
Received 25 February 2003
Copyright © 2004 Victor Rotger. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider principally polarized abelian varieties with quaternionic multiplication over number fields and we study the field of moduli of their endomorphisms in relation to the set of rational points on suitable Shimura varieties.