Moduli of Supersingular Abelian Varieties: 1680 (Lecture Notes in Mathematics)

by Frans Oort (Author), Frans Oort (Author), Ke-Zheng Li (Author)

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  Paperback
  2008

  $29.16

  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 AEg.g/4UE, 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).