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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Modular Shimura varieties and forgetful maps
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by Victor Rotger PDF
Trans. Amer. Math. Soc. 356 (2004), 1535-1550 Request permission

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
  • MR Author ID: 698263
  • Email: vrotger@mat.upc.es
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 1535-1550
  • MSC (2000): Primary 11G18, 14G35
  • DOI: https://doi.org/10.1090/S0002-9947-03-03408-1
  • MathSciNet review: 2034317