Moduli of Supersingular Abelian Varieties

von Ke-Zheng Li, Frans Oort

116 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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).

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783540639237
• Sprache: Englisch
• Erscheinungsdatum: 19.01.1998
• Genre: Mathematik/Arithmetik, Algebra
• Verlag: Springer Berlin