Lecture Notes in Mathematics

Li, Ke-Zheng; Oort, Frans

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).

Details

Published by: Springer

Publication Date: 1998-01-19

Format: Paperback

ISBN-13: 9783540639237

DOI: 10.1007/BFb0095931

Dimensions: 234cm x156cm

Pages: 116