Complex Multiplication and Lifting Problems
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A01=Brian Conrad
A01=Ching-Li Chai
A01=Frans Oort
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Author_Brian Conrad
Author_Ching-Li Chai
Author_Frans Oort
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Product details
- ISBN 9781470410148
- Weight: 860g
- Dimensions: 178 x 254mm
- Publication Date: 30 Jan 2014
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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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.
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.
Ching-Li Chai, University of Pennsylvania, Philadelphia, PA, USA
Brian Conrad, Stanford University, CA, USA
Frans Oort, University of Utrecht, The Netherlands
Brian Conrad, Stanford University, CA, USA
Frans Oort, University of Utrecht, The Netherlands
