On CM abelian varieties over an imaginary quadratic field

Abstract: In this talk, we will first show that a CM abelian variety over a quadratic imaginary field K has to have dimension at least h --- the ideal class number of K. We classify the CM abelian CM varieties of the dimension h over K. Finally, we associate one or two `simplest' CM abelian varieties over K of dimension h and prove their central L-value/derivative behaves amazingly well.