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The Arithmetic of Certain Calabi-Yau Varieties over Number Fields

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The Arithmetic and Geometry of Algebraic Cycles

Part of the book series: NATO Science Series ((ASIC,volume 548))

Abstract

We discuss questions of arithmetic nature for Calabi-Yau varieties of dimension ≤ 3. We first construct Calabi-Yau varieties as orbifolds of diagonal (Fermat) hypersurfaces in weighted projective spaces, and then determine their L-series. Further, several conjectures of arithmetic nature, e.g., the modularity conjecture for rigid Calabi-Yau threefolds defined over ℚ, and Shafarevich’s conjecture for CM-type Calabi-Yau varieties are discussed.

Received: February 2, 1999; Accepted: September 24, 1999

1991 Mathematics Subject Classification. 14J32, 11G40

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    Noriko Yui

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  1. Noriko Yui
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Editor information

Editors and Affiliations

  1. University of Oklahoma, Norman, Oklahoma, USA

    B. Brent Gordon

  2. University of Alberta, Edmonton, Alberta, Canada

    James D. Lewis

  3. Universität-GH-Essen, Essen, Germany

    Stefan Müller-Stach

  4. Tokyo Institute of Technology, Tokyo, Japan

    Shuji Saito

  5. Queen’s University, Kingston, Ontario, Canada

    Noriko Yui

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Yui, N. (2000). The Arithmetic of Certain Calabi-Yau Varieties over Number Fields. In: Gordon, B.B., Lewis, J.D., Müller-Stach, S., Saito, S., Yui, N. (eds) The Arithmetic and Geometry of Algebraic Cycles. NATO Science Series, vol 548. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4098-0_20

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  • DOI: https://doi.org/10.1007/978-94-011-4098-0_20

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  • Print ISBN: 978-0-7923-6194-7

  • Online ISBN: 978-94-011-4098-0

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