Abelian varieties with complex multiplication exist at the origin of class field theory, and they also play a central role in the contemporary theory of Shimura varieties. This book explores the relationship between such Abelian varieties over finite fields and over arithmetically interesting fields. 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 of how modern techniques in arithmetic geometry can combined with class field theory to answer concrete questions about Abelian varieties. It is a useful reference for researchers at the interface of number theory and algebraic geometry lifting problems Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)