Moduli of Supersingular Abelian Varieties

Ke-Zheng Li, Frans Oort (Autoren)

Buch | Softcover

IX, 116 Seiten

1998 | 1998
Springer Berlin (Verlag)
978-3-540-63923-7 (ISBN)

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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).

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.

Erscheint lt. Verlag	19.1.1998
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	IX, 116 p.
Verlagsort	Berlin
Sprache	englisch
Maße	156 x 234 mm
Gewicht	200 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Abelian varieties • abelian variety • Abelsche Mannigfaltigkeit • Algebraic Geometry • class numbers • COND042 • Dieudonn modules • Dimension • Hardcover, Softcover / Mathematik/Arithmetik, Algebra • HC/Mathematik/Arithmetik, Algebra • moduli
ISBN-10	3-540-63923-3 / 3540639233
ISBN-13	978-3-540-63923-7 / 9783540639237
Zustand	Neuware