Title: Moduli of supersingular abelian varieties /
Authors: Li, Ke-Zheng, 1949-; Oort, Frans, 1935-
Publisher: Springer,
Year: 1998
Subjects: Abelian varieties.; Algebraic varieties Classification theory.; Moduli theory.; Mathematics; Geometry, algebraic.
Abstract: 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: Introduction -- Supersingular abelian varieties -- Some prerequisites about group schemes -- Flag type quotients -- Main results on Sg,1 (the principally polarized case) -- Prerequisites about Dieudonne modules -- PFTQs of Dieudonné modules over W -- Moduli of rigid PFTQs of Dieudonné modules -- Some class numbers -- Examples on Sg,1 -- Main results on Sg,d (the non-principally polarized case) -- Proofs of the propositions on FTQs -- Examples on Sg,d (d>1) -- A scheme-theoretic definition of supersingularity -- Appendix: Some historical remarks -- References -- Index.