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.

 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). 

 Supersingular abelian varieties -- Some prerequisites about group schemes -- Flag type quotients -- Main results on S g,1 -- Prerequisites about Dieudonné modules -- PFTQs of Dieudonné modules over W -- Moduli of rigid PFTQs of Dieudonné modules -- Some class numbers -- Examples on S g,1 -- Main results on S g,d -- Proofs of the propositions on FTQs -- Examples on S g,d (d>1) -- A scheme-theoretic definition of supersingularity.