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Catalogue Information
Field name	Details
Dewey Class	516.35
Title	Moduli of Supersingular Abelian Varieties ([EBook]) / by Ke-Zheng Li, Frans Oort.
Author	Li, Ke-Zheng
Added Personal Name	Oort, Frans. , 1935-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1998.
Physical Details	IX, 116 pages : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1680
ISBN	9783540696667
Summary Note	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).:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0095931
Links to Related Works	Subject References: Algebraic Geometry . Mathematics . Authors: author . Li, Ke-Zheng . Oort, Frans. 1935- . oort, Frans, 1935- . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 516.35 .

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Moduli of Supersingular Abelian Varieties

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