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Hodge cycles on abelian varieties associated to the complete binary trees. (English) Zbl 1117.14013

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.

MSC:

14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
11G10 Abelian varieties of dimension \(> 1\)
06A11 Algebraic aspects of posets
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