Chai, ChingLi
Overview
Works:  12 works in 71 publications in 2 languages and 2,485 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA564, 516.353 
Publication Timeline
.
Most widely held works by
ChingLi Chai
Degeneration of Abelian varieties by
Gerd Faltings(
Book
)
16 editions published between 1990 and 2011 in English and Spanish and held by 414 WorldCat member libraries worldwide
This book presents a complete treatment of semiabelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space. Most results are new and have never been published before. Highlights of the book include a classification of semiabelian 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. The book also provides a new approach to Siegel modular forms. This work should serve as a valuable reference source for researchers and graduate students interested in algebraic geometry, Shimura varieties, or diophantine geometry
16 editions published between 1990 and 2011 in English and Spanish and held by 414 WorldCat member libraries worldwide
This book presents a complete treatment of semiabelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space. Most results are new and have never been published before. Highlights of the book include a classification of semiabelian 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. The book also provides a new approach to Siegel modular forms. This work should serve as a valuable reference source for researchers and graduate students interested in algebraic geometry, Shimura varieties, or diophantine geometry
Compactification of Siegel moduli schemes by
ChingLi Chai(
Book
)
3 editions published in 1985 in English and held by 281 WorldCat member libraries worldwide
The Siegel moduli scheme classifies principally polarised abelian varieties and its compactification is an important result in arithmetic algebraic geometry. The main result of this monograph is to prove the existence of the toroidal compactification over Z (1/2). This result should have further applications and is presented here with sufficient background material to make the book suitable for seminar courses in algebraic geometry, algebraic number theory or automorphic forms
3 editions published in 1985 in English and held by 281 WorldCat member libraries worldwide
The Siegel moduli scheme classifies principally polarised abelian varieties and its compactification is an important result in arithmetic algebraic geometry. The main result of this monograph is to prove the existence of the toroidal compactification over Z (1/2). This result should have further applications and is presented here with sufficient background material to make the book suitable for seminar courses in algebraic geometry, algebraic number theory or automorphic forms
Complex multiplication and lifting problems by
ChingLi Chai(
Book
)
9 editions published in 2014 in English and held by 216 WorldCat member libraries worldwide
Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to illustrate the general theory and present a detailed treatment of many fundamental results and concepts in the arithmetic of abelian varieties, such as the Main Theorem of Complex Multiplication and its generalizations, the finer aspects of Tate's work on abelian varieties over finite fields, and deformation theory. This book provides an ideal illustration of how modern techniques in arithmetic geometry (such as descent theory, crystalline methods, and group schemes) can be fruitfully combined with class field theory to answer concrete questions about abelian varieties. It will be a useful reference for researchers and advanced graduate students at the interface of number theory and algebraic geometry.  Provided by publisher
9 editions published in 2014 in English and held by 216 WorldCat member libraries worldwide
Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to illustrate the general theory and present a detailed treatment of many fundamental results and concepts in the arithmetic of abelian varieties, such as the Main Theorem of Complex Multiplication and its generalizations, the finer aspects of Tate's work on abelian varieties over finite fields, and deformation theory. This book provides an ideal illustration of how modern techniques in arithmetic geometry (such as descent theory, crystalline methods, and group schemes) can be fruitfully combined with class field theory to answer concrete questions about abelian varieties. It will be a useful reference for researchers and advanced graduate students at the interface of number theory and algebraic geometry.  Provided by publisher
Selected papers on the classification of varieties and moduli spaces by
David Mumford(
Book
)
2 editions published in 2010 in English and held by 149 WorldCat member libraries worldwide
2 editions published in 2010 in English and held by 149 WorldCat member libraries worldwide
Algebra and geometry : proceedings of the International Conference of Algebra and Geometry : National Taiwan University, December
2630, 1995 by International Conference of Algebra and Geometry(
Book
)
6 editions published in 1998 in English and held by 78 WorldCat member libraries worldwide
6 editions published in 1998 in English and held by 78 WorldCat member libraries worldwide
Selected papers by
David Mumford(
Book
)
10 editions published in 2010 in English and held by 71 WorldCat member libraries worldwide
10 editions published in 2010 in English and held by 71 WorldCat member libraries worldwide
Compactification of Siegel moduli schemes by
ChingLi Chai(
Book
)
19 editions published between 1984 and 1999 in English and held by 59 WorldCat member libraries worldwide
19 editions published between 1984 and 1999 in English and held by 59 WorldCat member libraries worldwide
A disaster response management system based on the control systems technology by X Liu(
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
CM liftings by
ChingLi Chai(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Hecke orbits as Shimura varieties in positive characteristic by
ChingLi Chai(
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Compactification of Siegel moduli chemes by
ChingLi Chai(
Book
)
2 editions published in 1984 in Undetermined and English and held by 1 WorldCat member library worldwide
2 editions published in 1984 in Undetermined and English and held by 1 WorldCat member library worldwide
Arithmetic geometry by
Gary Cornell(
)
1 edition published in 1986 in English and held by 0 WorldCat member libraries worldwide
This book is the result of a conference on arithmetic geometry, held July 30 through August 10, 1984 at the University of Connecticut at Storrs, the purpose of which was to provide a coherent overview of the subject. This subject has enjoyed a resurgence in popularity due in part to Faltings' proof of Mordell's conjecture. Included are extended versions of almost all of the instructional lectures and, in addition, a translation into English of Faltings' groundbreaking paper. ARITHMETIC GEOMETRY should be of great use to students wishing to enter this field, as well as those already working in it. This revised second printing now includes a comprehensive index
1 edition published in 1986 in English and held by 0 WorldCat member libraries worldwide
This book is the result of a conference on arithmetic geometry, held July 30 through August 10, 1984 at the University of Connecticut at Storrs, the purpose of which was to provide a coherent overview of the subject. This subject has enjoyed a resurgence in popularity due in part to Faltings' proof of Mordell's conjecture. Included are extended versions of almost all of the instructional lectures and, in addition, a translation into English of Faltings' groundbreaking paper. ARITHMETIC GEOMETRY should be of great use to students wishing to enter this field, as well as those already working in it. This revised second printing now includes a comprehensive index
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Associated Subjects
Abelian varieties Algebra Algebraic number theory Algebraic varietiesClassification theory Arithmetical algebraic geometry Compactifications Forms, Modular Functions, Theta Geometry Geometry, Algebraic Mathematics Moduli theory Multiplication, Complex Number theory Surfaces, AlgebraicDegenerations