Abstract
We study bounds of the rank of CM-types of CM-fields, and using the bounds, we show that all CM-types of Galois CM-fields with cyclic or dicyclic Galois groups of order 2kp with a prime p are nondegenerate. We also show the nondegeneracy of CM-types for certain non-Galois CM-fields. As a consequence, the Hodge conjecture is true for abelian varieties with complex multiplication by such CM-fields.
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