Shimura curves embedded in Igusa's threefold

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

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Number Theory, Algebraic Geometry, 11G18; 14G35

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http://salesiana.dossiersoluciones.com/handle/123456789/69693

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312435
 http://arxiv.org/abs/math/0312435

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arXiv