On the rank of CM-Type

Abstract

In the present note, we prove that every simple CM-type is non-degenerate (i.e. the rank is maximal) if the dimension of corresponding abelian varieties is a prime. This follows directly from the argument of Tankeev [5], in which he has treated the 5-dimensional case.Recently, S. G. Tankeev and K. A. Ribet have established similar results for more general types of abelian varieties (see [3], [4], [6]).