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Modular Shimura varieties and forgetful maps

Author(s): Victor Rotger
Journal: Trans. Amer. Math. Soc. 356 (2004), 1535-1550.
MSC (2000): Primary 11G18, 14G35
Posted: October 6, 2003
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Abstract: In this note we consider several maps that occur naturally between modular Shimura varieties, Hilbert-Blumenthal varieties and the moduli spaces of polarized abelian varieties when forgetting certain endomorphism structures. We prove that, up to birational equivalences, these forgetful maps coincide with the natural projection by suitable abelian groups of Atkin-Lehner involutions.

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Additional Information:

Victor Rotger
Affiliation: Universitat Politècnica de Catalunya, Departament de Matemàtica Aplicada IV (EUPVG), Av. Victor Balaguer s/n, 08800 Vilanova i la Geltrú, Spain
Email: vrotger@mat.upc.es

DOI: 10.1090/S0002-9947-03-03408-1
PII: S 0002-9947(03)03408-1
Keywords: Shimura variety, moduli space, abelian variety, quaternion algebra
Received by editor(s): August 19, 2002
Received by editor(s) in revised form: February 12, 2003
Posted: October 6, 2003
Additional Notes: This research was partially supported by a grant FPI from the Ministerio de Ciencia y Tecnología BFM2000-0627
Copyright of article: Copyright 2003, American Mathematical Society

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