Hodge cycles on abelian varieties associated to the complete binary trees (Q819558)

This paper is an investigation of the structure of the ring of Hodge cycles on a complex abelian variety \(A\) of CM-type, where the CM-field \(K\) is Galois over \(\mathbb Q\) with Galois group isomorphic to \(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2^n\mathbb{Z}\). The author constructs all degenerate CM-types for \(K\), and enumerates the Hodge cycles on the associated abelian varieties. These results are obtained as applications of combinatorial results on complete binary trees.