Shimura curves embedded in Igusa's threefold

Details Shimura curves embedded in Igusa's threefold Shimura curves embedded in Igusa's threefold

2003-12-23

arxiv.org/abs/math/0312435v1

Mathematics

Number Theory

To appear in Modular curves and Abelian varieties, Progress in Mathematics 224 Birkhauser, (2003), 263-273

Scientific paper

Let 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.

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