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

Hazama, Fumio

J. Math. Soc. Japan 58, No. 1, 55-82 (2006).

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.

Reviewer: Salman Abdulali (Greenville)

MSC:

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

Keywords:

Hodge cycle; abelian variety; binary tree