Item Details
Complex Multiplication and Lifting Problems
ChingLi Chai, Brian Conrad, Frans Oort
 Format
 Book
 Published
 Providence, Rhode Island : American Mathematical Society, [2014]
 Language
 English
 Series
 Mathematical Surveys and Monographs
 ISBN
 9781470410148, 1470410141
 Summary
 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.
 Description
 ix, 387 pages ; 26 cm.
 Notes
 Includes bibliographical references (pages 379383) and index.
 Series Statement
 Mathematical surveys and monographs ; volume 195
 Mathematical surveys and monographs ; no. 195
 Technical Details

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LEADER 02785cam a2200421 i 4500001 u6190305003 SIRSI005 20140131114916.0008 130912s2014 riua b 001 0 enga 2013036892a 9781470410148 q alkaline papera 1470410141 q alkaline papera (OCoLC)858778275a pcca DLC b eng e rda c DLC d YDX d OCLCO d BTCTA d YDXCP d ORC d OCLCO d IQU d HF9a QA564 b .C44 2014a 516.3/53 2 23a 11G15 a 14K02 a 14L05 a 14K15 a 14D15 2 msca Chai, ChingLi, e author.a Complex multiplication and lifting problems / c ChingLi Chai, Brian Conrad, Frans Oort.a Providence, Rhode Island : b American Mathematical Society, c [2014]a ix, 387 pages ; c 26 cm.a text 2 rdacontenta unmediated 2 rdamediaa volume 2 rdacarriera Mathematical surveys and monographs ; v volume 195a Includes bibliographical references (pages 379383) and index.a 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.a Multiplication, Complex.a Abelian varieties.a Lifting theory.a Conrad, Brian, d 1970 e author.a Oort, Frans, d 1935 e author.a Mathematical surveys and monographs ; v no. 195.a Z0 b VA@a 8a QA564 .C44 2014 w LC i X031624086 l STACKS m MATH t BOOK
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