Li Ke-Zheng, Frans Oort

Moduli of Supersingular Abelian Varieties

• Broschiertes Buch

Produktbeschreibung

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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Produktdetails

• Lecture Notes in Mathematics 1680
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-63923-7
• 1998.
• Seitenzahl: 124
• Erscheinungstermin: 19. Januar 1998
• Englisch
• Abmessung: 235mm x 155mm x 8mm
• Gewicht: 454g
• ISBN-13: 9783540639237
• ISBN-10: 3540639233
• Artikelnr.: 09233383

Inhaltsangabe

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.