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Moduli of Supersingular Abelian Varieties

  • Authors
  • Ke-Zheng Li
  • Frans Oort

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

Table of contents

  1. Front Matter
    Pages I-V
  2. Ke-Zheng Li, Frans Oort
    Pages 1-10
  3. Ke-Zheng Li, Frans Oort
    Pages 11-15
  4. Ke-Zheng Li, Frans Oort
    Pages 16-18
  5. Ke-Zheng Li, Frans Oort
    Pages 19-23
  6. Ke-Zheng Li, Frans Oort
    Pages 24-27
  7. Ke-Zheng Li, Frans Oort
    Pages 28-34
  8. Ke-Zheng Li, Frans Oort
    Pages 35-38
  9. Ke-Zheng Li, Frans Oort
    Pages 39-50
  10. Ke-Zheng Li, Frans Oort
    Pages 51-54
  11. Ke-Zheng Li, Frans Oort
    Pages 55-68
  12. Ke-Zheng Li, Frans Oort
    Pages 69-72
  13. Ke-Zheng Li, Frans Oort
    Pages 73-83
  14. Ke-Zheng Li, Frans Oort
    Pages 84-86
  15. Ke-Zheng Li, Frans Oort
    Pages 87-95
  16. Back Matter
    Pages 96-118

About this book

Introduction

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).

Keywords

Abelian varieties Abelian variety Dieudonn modules Dimension algebraic geometry class numbers moduli

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0095931
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63923-7
  • Online ISBN 978-3-540-69666-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site