Moduli of supersingular Abelian varieties
著者
書誌事項
Moduli of supersingular Abelian varieties
（Lecture notes in mathematics, 1680）
Springer, c1998
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注記
Includes bibliographical references (p. 106-111) and index
内容説明・目次
内容説明
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 AEg.g/4UE, 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).
目次
Supersingular abelian varieties.- Some prerequisites about group schemes.- Flag type quotients.- Main results on S g,1.- Prerequisites about Dieudonne modules.- PFTQs of Dieudonne modules over W.- Moduli of rigid PFTQs of Dieudonne 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.
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