Moduli of Supersingular Abelian Varieties (Lecture Notes in Mathematics)

By Frans Oort and Ke-Zheng Li

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).

• Format: Paperback
• Language: English
• ISBN: 3540639233
• ISBN13: 9783540639237
• Release Date: January 1998
• Publisher: Springer
• Length: 116 Pages
• Weight: 0.44 lbs.
• Dimensions: 0.3" x 6.1" x 9.2"