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The Arithmetic and Geometry of Algebraic Cycles pp 495–513Cite as

Reduction of Abelian Varieties

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

Abstract

In this paper we study the reduction of abelian varieties. In particular, we study the relationships between n-torsion points onXand the reduction of X, where X is an abelian variety over a field F with a discrete valuation, and n is an integer not divisible by the residue characteristic.

Key words

  • abelian varieties
  • semistable reduction
  • torsion points

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ohio State University, 231 W. 18 Avenue, Columbus, Ohio, 43210-1174, USA

    A. Silverberg

  2. Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Yu. G. Zarhin

Authors
  1. A. Silverberg
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  2. Yu. G. Zarhin
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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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Silverberg, A., Zarhin, Y.G. (2000). Reduction of Abelian Varieties. 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_19

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  • DOI: https://doi.org/10.1007/978-94-011-4098-0_19

  • 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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