2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69693Let O be a maximal order in a totally indefinite quaternion algebra over a totally real number field. In this note we study the locus Q_O of quaternionic multiplication by O in the moduli space A_g of principally polarized abelian varieties of even dimension g with particular emphasis in the two-dimensional case. We describe Q_O as a union of Atkin-Lehner quotients of Shimura varieties and we compute the number of irreducible components of Q_O in terms of class numbers of CM-fields.To appear in Modular curves and Abelian varieties, Progress in Mathematics 224 Birkhauser, (2003), 263-273Number TheoryAlgebraic Geometry11G18; 14G35text