Moduli of Supersingular Abelian Varieties
Li, Ke-Zheng.
Moduli of Supersingular Abelian Varieties [electronic resource] / by Ke-Zheng Li, Frans Oort. - IX, 116 p. online resource. - Lecture Notes in Mathematics, 1680 0075-8434 ; . - Lecture Notes in Mathematics, 1680 .
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).
9783540696667
10.1007/BFb0095931 doi
Geometry, algebraic.
Algebraic Geometry.
QA564-609
516.35
Moduli of Supersingular Abelian Varieties [electronic resource] / by Ke-Zheng Li, Frans Oort. - IX, 116 p. online resource. - Lecture Notes in Mathematics, 1680 0075-8434 ; . - Lecture Notes in Mathematics, 1680 .
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).
9783540696667
10.1007/BFb0095931 doi
Geometry, algebraic.
Algebraic Geometry.
QA564-609
516.35