Moduli of supersingular Abelian varieties
Ke-Zheng Li, Frans Oort.
Bok Engelsk 1998 · Electronic books.
| Medvirkende | Oort, Frans, (author.)
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|---|---|
| Omfang | 1 online resource (IX, 116 p.)
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| Utgave | 1st ed. 1998.
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| Opplysninger | Bibliographic Level Mode of Issuance: Monograph. - 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.. - 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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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 3-540-69666-0
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