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Moduli of Supersingular Abelian Varieties

  • Book
  • © 1998

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Authors:
  1. Ke-Zheng Li
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    You can also search for this author in PubMed   Google Scholar

  2. Frans Oort
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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1680)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-V
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  2. Introduction

    • Ke-Zheng Li, Frans Oort
    Pages 1-10

  3. Supersingular abelian varieties

    • Ke-Zheng Li, Frans Oort
    Pages 11-15

  4. Some prerequisites about group schemes

    • Ke-Zheng Li, Frans Oort
    Pages 16-18

  5. Flag type quotients

    • Ke-Zheng Li, Frans Oort
    Pages 19-23

  6. Main results on S g,1

    • Ke-Zheng Li, Frans Oort
    Pages 24-27

  7. Prerequisites about Dieudonné modules

    • Ke-Zheng Li, Frans Oort
    Pages 28-34

  8. PFTQs of Dieudonné modules over W

    • Ke-Zheng Li, Frans Oort
    Pages 35-38

  9. Moduli of rigid PFTQs of Dieudonné modules

    • Ke-Zheng Li, Frans Oort
    Pages 39-50

  10. Some class numbers

    • Ke-Zheng Li, Frans Oort
    Pages 51-54

  11. Examples on S g,1

    • Ke-Zheng Li, Frans Oort
    Pages 55-68

  12. Main results on S g,d

    • Ke-Zheng Li, Frans Oort
    Pages 69-72

  13. Proofs of the propositions on FTQs

    • Ke-Zheng Li, Frans Oort
    Pages 73-83

  14. Examples on S g,d (d>1)

    • Ke-Zheng Li, Frans Oort
    Pages 84-86

  15. A scheme-theoretic definition of supersingularity

    • Ke-Zheng Li, Frans Oort
    Pages 87-95

  16. Back Matter

    Pages 96-118
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Keywords

About this book

Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to Äg.g/4Ü, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).

Bibliographic Information

  • Book Title: Moduli of Supersingular Abelian Varieties

  • Authors: Ke-Zheng Li, Frans Oort

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0095931

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-63923-7Published: 19 January 1998

  • eBook ISBN: 978-3-540-69666-7Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 116

  • Topics: Algebraic Geometry

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