Moduli of Supersingular Abelian Varieties

Moduli of Supersingular Abelian Varieties PDF

Author: Ke-Zheng Li

Publisher: Springer

Published: 2006-11-14

Total Pages: 123

ISBN-13: 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 Abelian Varieties

Moduli of Abelian Varieties PDF

Author: Gerard van der Geer

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 526

ISBN-13: 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 PDF

Author: Carel Faber

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 205

ISBN-13: 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.

Modular Curves and Abelian Varieties

Modular Curves and Abelian Varieties PDF

Author: John Cremona

Publisher: Springer Science & Business Media

Published: 2004-02-23

Total Pages: 308

ISBN-13: 9783764365868

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This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matemàtica (Bellaterra, Barcelona). The articles in this volume present the latest achievements in this extremely active field and will be of interest both to specialists and to students and researchers. Many contributions focus on generalizations of the Shimura-Taniyama conjecture to varieties such as elliptic Q-curves and Abelian varieties of GL_2-type. The book also includes several key articles in the subject that do not correspond to conference lectures.

Moduli of Abelian Varieties

Moduli of Abelian Varieties PDF

Author: Gerard van der Geer

Publisher: Birkhäuser

Published: 2012-10-23

Total Pages: 518

ISBN-13: 9783034895095

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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.

The Arithmetic and Geometry of Algebraic Cycles

The Arithmetic and Geometry of Algebraic Cycles PDF

Author: B. Brent Gordon

Publisher: American Mathematical Soc.

Published: 2000-01-01

Total Pages: 468

ISBN-13: 9780821870204

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From the June 1998 Summer School come 20 contributions that explore algebraic cycles (a subfield of algebraic geometry) from a variety of perspectives. The papers have been organized into sections on cohomological methods, Chow groups and motives, and arithmetic methods. Some specific topics include logarithmic Hodge structures and classifying spaces; Bloch's conjecture and the K-theory of projective surfaces; and torsion zero-cycles and the Abel-Jacobi map over the real numbers.

Rationality of Varieties

Rationality of Varieties PDF

Author: Gavril Farkas

Publisher: Springer Nature

Published: 2021-10-19

Total Pages: 433

ISBN-13: 3030754219

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This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on varieties, contributed by the foremost experts in their fields. The question of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a long history and played an important role in the history of algebraic geometry. Recent developments in algebraic geometry have made this question again a focal point of research and formed the impetus to organize a conference in the series of conferences on the island of Schiermonnikoog. The book follows in the tradition of earlier volumes, which originated from conferences on the islands Texel and Schiermonnikoog.

Algebraic Geometry And Algebraic Number Theory -Procs Of The Spcial Prg At The Nankai Institute Of Maths

Algebraic Geometry And Algebraic Number Theory -Procs Of The Spcial Prg At The Nankai Institute Of Maths PDF

Author: Ke-qin Feng

Publisher: World Scientific

Published: 1992-12-11

Total Pages: 229

ISBN-13: 9814554987

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This volume contains 18 research papers on algebraic geometry, algebraic number theory and algebraic groups. Two summarized surveys on Arthur's invariant trace formula and the representation theory of quantum linear groups by K F Lai and Jian-Pan Wang respectively are included.

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