Talk 1:  Basic properties of CM abelian varieties

Abstract:  The theory of abelian varieties with complex multiplication
is a natural generalization of the theory of CM elliptic curves, but it exhibits
a richer structure than can be perceived in the 1-dimensional case.
In this expository talk we will explain some basic notions in the theory
(such as reflex fields, CM types, and the Shimura-Taniyama formula) and we
discuss special features when the ground field is the complex field or a finite field.