Moduli of Supersingular Abelian Varieties (Lecture Notes in Mathematics)
Edition: 1 edition
Publisher: Springer
Published: March 5, 1998
Language: eng
Format: Paperback
Number of pages: 116
ISBN-13: 9783540639237
Subjects: Algebraic Geometry; Mathematics; Science/Mathematics; Moduli theory; Geometry - Algebraic; Dieudonn modules; Mathematics / Geometry / Algebraic; class numbers; moduli; Abelian varieties; Algebraic varieties; Classification theory
Description: 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).