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 ?g.g/4?, 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).
| Author: Ke-Zheng Li |
| Publisher: Springer |
| Publication Date: Jan 19, 1998 |
| Number of Pages: 116 pages |
| Binding: Paperback or Softback |
| ISBN-10: 3540639233 |
| ISBN-13: 9783540639237 |
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