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portada Complex Multiplication and Lifting Problems
Type
Physical Book
Publisher
Author
Collection
Mathematical Surveys and Monographs
Year
2014
Language
English
Pages
387
Format
Hardcover
Dimensions
25.40 x 17.80 cm
ISBN13
9781470410148

Complex Multiplication and Lifting Problems

Brian Conrad;Frans Oort;Ching-Li Chai (Author) · American Mathematical Society · Hardcover

Complex Multiplication and Lifting Problems - Brian Conrad;Frans Oort;Ching-Li Chai

New Book Imported to South Africa
Delivery: 25 Aug - 03 Sep Shipping: 7 to 8 business days.
R 2,749
R 2,749

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Synopsis "Complex Multiplication and Lifting Problems"

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 generalisations, 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.

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