Moduli of Supersingular Abelian Varieties

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).

Sommario

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.

Dettagli sul prodotto

• Autori: Ke-Zhen Li, Ke-zheng Li, Li Ke-Zheng, Frans Oort
• Editore: Springer, Berlin
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 17.10.2001
• EAN: 9783540639237
• ISBN: 978-3-540-63923-7
• Pagine: 116
• Dimensioni: 143 mm x 236 mm x 9 mm
• Peso: 454 g
• Illustrazioni: IX, 116 p.
• Serie: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Categoria: Scienze naturali, medicina, informatica, tecnica > Matematica > Aritmetica, algebra