TY  - BOOK
AU  - Chai,Ching-Li
AU  - Conrad,Brian
AU  - Oort,Frans
TI  - Complex multiplication and lifting problems
T2  - Mathematical surveys and monographs
SN  - 9781470410148 (alk. paper)
U1  - 510MS 23
PY  - 2014///
CY  - Providence
PB  - American Mathematical Society
KW  - Complex Multiplication
KW  - Abelian varieties
N1  - Includes bibliographical references (pages 379-383) and index; Preface --
 Introduction --
 References --
 Notation and terminology - 
1. Algebraic Theory of Complex Multiplication --
2. CM lifting over a discrete valuation ring --
3. CM lifting of p-divisible groups --
4. CM Lifting of abelian varieties up to isogeny --
Appendix A: Some arithmetic results for abelian varieties --
Appendix B. CM lifting via p-adic Hodge theory --
Notes on Quotes --
Glossary of Notations --
Bibliography --
Index
N2  - 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
ER  -