Moduli of Supersingular Abelian Varieties (Lecture Notes in Mathematics)

Ke-Zheng Li, Frans Oort

ISBN 10: 3540639233 / ISBN 13: 9783540639237

Published by Springer 2008-06-13, 2008

About this Item

Seller Inventory # 6666-IUK-9783540639237

Bibliographic Details

• Title: Moduli of Supersingular Abelian Varieties (Lecture Notes in Mathematics)
• Publisher: Springer 2008-06-13
• Publication Date: 2008
• Language: English
• ISBN 10: 3540639233
• ISBN 13: 9783540639237
• Binding: Paperback
• Condition: New

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).