Moduli of Supersingular Abelian Varieties

Moduli of Supersingular Abelian Varieties
Title Moduli of Supersingular Abelian Varieties PDF eBook
Author Ke-Zheng Li
Publisher Springer
Pages 123
Release 2006-11-14
Genre 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).

Moduli of Supersingular Abelian Varieties

Moduli of Supersingular Abelian Varieties
Title Moduli of Supersingular Abelian Varieties PDF eBook
Author Ke-Zheng Li
Publisher Springer Science & Business Media
Pages 140
Release 1998-01-19
Genre Mathematics
ISBN 9783540639237

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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 Ãg.g/4Ã, 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).

Moduli of Supersingular Abelian Varieties

Moduli of Supersingular Abelian Varieties
Title Moduli of Supersingular Abelian Varieties PDF eBook
Author Ke-Zheng Li
Publisher
Pages 138
Release 2014-01-15
Genre
ISBN 9783662211793

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Moduli of Abelian Varieties

Moduli of Abelian Varieties
Title Moduli of Abelian Varieties PDF eBook
Author Gerard van der Geer
Publisher Birkhäuser
Pages 526
Release 2012-12-06
Genre Mathematics
ISBN 303488303X

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Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.

Moduli of Curves and Abelian Varieties

Moduli of Curves and Abelian Varieties
Title Moduli of Curves and Abelian Varieties PDF eBook
Author Carel Faber
Publisher Springer Science & Business Media
Pages 205
Release 2012-12-06
Genre Technology & Engineering
ISBN 3322901726

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The Dutch Intercity Seminar on Moduli, which dates back to the early eighties, was an initiative of G. van der Geer, F. Oort and C. Peters. Through the years it became a focal point of Dutch mathematics and it gained some fame, also outside Holland, as an active biweekly research seminar. The tradition continues up to today. The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Hain, E. Looijenga, and F. Oort, originates from the seminar held in 1995--96. Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles.

Moduli of Supersingular Abelian Varieties

Moduli of Supersingular Abelian Varieties
Title Moduli of Supersingular Abelian Varieties PDF eBook
Author K.-Z. Li
Publisher
Pages 107
Release 1993
Genre
ISBN

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The Arithmetic and Geometry of Algebraic Cycles

The Arithmetic and Geometry of Algebraic Cycles
Title The Arithmetic and Geometry of Algebraic Cycles PDF eBook
Author B. Brent Gordon
Publisher American Mathematical Soc.
Pages 462
Release 2000
Genre Mathematics
ISBN 0821819542

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The NATO ASI/CRM Summer School at Banff offered a unique, full, and in-depth account of the topic, ranging from introductory courses by leading experts to discussions of the latest developments by all participants. The papers have been organized into three categories: cohomological methods; Chow groups and motives; and arithmetic methods.As a subfield of algebraic geometry, the theory of algebraic cycles has gone through various interactions with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to developments such as a description of Chow groups in terms of algebraic K-theory, the application of the Merkurjev-Suslin theorem to the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge, and of Tate, which compute cycles classgroups respectively in terms of Hodge theory or as the invariants of a Galois group action on étale cohomology, the conjectures of Bloch and Beilinson, which explain the zero or pole of the $L$-function of a variety and interpret the leading non-zero coefficient of its Taylor expansion at a criticalpoint, in terms of arithmetic and geometric invariant of the variety and its cycle class groups.The immense recent progress in the theory of algebraic cycles is based on its many interactions with several other areas of mathematics. This conference was the first to focus on both arithmetic and geometric aspects of algebraic cycles. It brought together leading experts to speak from their various points of view. A unique opportunity was created to explore and view the depth and the breadth of the subject. This volume presents the intriguing results.