Moduli of Supersingular Abelian Varieties

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...

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Bibliographic Details
Main Authors: Li, Ke-Zheng, Oort, Frans
Format: Book
Language:English
Subjects:
Abelian varieties
Algebraic Geometry
Algebraic varieties
Geometry, Algebraic
Mathematics
Mathematics and Statistics
Moduli theory
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Summary: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).
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0095931