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Shimura Curves Embedded in Igusa’s Threefold

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Modular Curves and Abelian Varieties

Part of the book series: Progress in Mathematics ((PM,volume 224))

Abstract

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 Qo of quaternionic multiplication by O in the moduli space A9 of principally polarized abelian varieties of even dimension g with particular emphasis in the two-dimensional case. We describe Qo as a union of Atkin-Lehner quotients of Shimura varieties and we compute the number of irreducible components of Qo in terms of class numbers of CM-fields.

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Authors and Affiliations

  1. Departament de Matemàtica Aplicada IV (EUPVG), Universitat Politècnica de Catalunya, Av. Victor Balaguer, 08800, Vilanova i la Geltrú, Spain

    Victor Rotger

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  1. Victor Rotger
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    John E. Cremona

  2. Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Pau Gargallo, 5, 08028, Barcelona, Spain

    Joan-Carles Lario  & Jordi Quer  & 

  3. Department of Mathematics, University of California, M/C 3840, Berkeley, CA, 94720-3840, USA

    Kenneth A. Ribet

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© 2004 Springer Basel AG

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Rotger, V. (2004). Shimura Curves Embedded in Igusa’s Threefold. In: Cremona, J.E., Lario, JC., Quer, J., Ribet, K.A. (eds) Modular Curves and Abelian Varieties. Progress in Mathematics, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7919-4_16

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  • DOI: https://doi.org/10.1007/978-3-0348-7919-4_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9621-4

  • Online ISBN: 978-3-0348-7919-4

  • eBook Packages: Springer Book Archive

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