[PDF] Classification Of Supersingular Abelian Varieties eBook

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Moduli of Supersingular Abelian Varieties

Ke-Zheng Li
Moduli of Supersingular Abelian Varieties by Ke-Zheng Li PDF

Author : Ke-Zheng Li
Publisher : Springer
Page : 123 pages
File Size : 18,62 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540696660

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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).

Degeneration of Abelian Varieties

Gerd Faltings
Degeneration of Abelian Varieties by Gerd Faltings PDF

Author : Gerd Faltings
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 30,24 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 3662026325

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A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.