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 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).

List of contents

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.

Product details

• Authors: Ke-Zhen Li, Ke-Zheng Li, Li Ke-Zheng, Frans Oort
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 17.10.2001
• EAN: 9783540639237
• ISBN: 978-3-540-63923-7
• No. of pages: 116
• Dimensions: 143 mm x 236 mm x 9 mm
• Weight: 454 g
• Illustrations: IX, 116 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra