𝔬K0-quasi-abelian varieties with complex multiplication

Abstract

We are interested in finding the relation between rings of endomorphisms of toroidal groups and algebraic number fields which are not totally real. For algebraic number fields K , we define real maximal algebraic number fields K 0 and 𝔬 K 0 -quasi-abelian varieties. We show that any simple 𝔬 K 0 -quasi-abelian variety is constructed by embeddings of a non-totally real algebraic number field K and it has finite dimensional cohomology groups.