Moduli of Supersingular Abelian Varieties: 1680 - Brossura

Li, Ke-Zheng; Oort, Frans

Brossura

ISBN 10: 3540639233 ISBN 13: 9783540639237

Casa editrice: Springer, 2008

Riassunto

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).

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Contenuti

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 Description

Book by Li KeZheng Oort Frans

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 3540639233
• ISBN 13: 9783540639237
• Rilegatura: Copertina flessibile
• Numero di pagine: 136
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania