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

Li, Ke-Zheng,Oort, Frans

ISBN 10: 3540639233 / ISBN 13: 9783540639237

Published by Springer, 1998

About this Item

Seller Inventory # 9783540639237-2-2

Bibliographic Details

• Title: Moduli of Supersingular Abelian Varieties (Lecture Notes in Mathematics, 1680)
• Publisher: Springer
• Publication Date: 1998
• Language: English
• ISBN 10: 3540639233
• ISBN 13: 9783540639237
• Binding: Soft cover
• Condition: Very good

About this title

Synopsis

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).