Author	Li, Ke-Zheng. author
Title	Moduli of Supersingular Abelian Varieties [electronic resource] / by Ke-Zheng Li, Frans Oort
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1998
Connect to	http://dx.doi.org/10.1007/BFb0095931
Descript	IX, 116 p. online resource

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 รg.g/4ร, 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)

Supersingular abelian varieties -- Some prerequisites about group schemes -- Flag type quotients -- Main results on S g,1 -- Prerequisites about Dieudonnรฉ modules -- PFTQs of Dieudonnรฉ modules over W -- Moduli of rigid PFTQs of Dieudonnรฉ 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

1. Mathematics
2. Algebraic geometry
3. Mathematics
4. Algebraic Geometry