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Kuga-Satake Varieties and the Hodge Conjecture

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The Arithmetic and Geometry of Algebraic Cycles

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

Abstract

Kuga-Satake varieties are abelian varieties associated to certain weight two Hodge structures, for example the second cohomology group of a K3 surface. We start with an introduction to Hodge structures and we give a detailed account of the construction of KugaSatake varieties. The Hodge conjecture is discussed in section2. An excellent survey of the Hodge conjecture for abelian varieties is [G].

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, Pavia, I-27100, Italia

    Bert van Geemen

Authors
  1. Bert van Geemen
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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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© 2000 Springer Science+Business Media Dordrecht

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van Geemen, B. (2000). Kuga-Satake Varieties and the Hodge Conjecture. 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_3

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  • DOI: https://doi.org/10.1007/978-94-011-4098-0_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6194-7

  • Online ISBN: 978-94-011-4098-0

  • eBook Packages: Springer Book Archive

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