Moduli of Supersingular Abelian Varieties

• Κύριοι συγγραφείς: Li, Ke-Zheng (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Oort, Frans (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.
• Έκδοση: 1st ed. 1998.
• Σειρά: Lecture Notes in Mathematics, 1680
• Θέματα: Algebraic geometry.; Algebraic Geometry.
• Φυσική περιγραφή: IX, 116 p. online resource.
• ISBN: 9783540696667
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0095931

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).