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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Modular Shimura varieties and forgetful maps


Author: Victor Rotger
Journal: Trans. Amer. Math. Soc. 356 (2004), 1535-1550
MSC (2000): Primary 11G18, 14G35
Published electronically: October 6, 2003
MathSciNet review: 2034317
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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: http://dx.doi.org/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
Published electronically: October 6, 2003
Additional Notes: This research was partially supported by a grant FPI from the Ministerio de Ciencia y Tecnología BFM2000-0627
Article copyright: © Copyright 2003 American Mathematical Society