International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 52, Pages 2795-2808

The field of moduli of quaternionic multiplication on abelian varieties

Victor Rotger

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.


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.