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.


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