Cycles of small codimension on a simple - or -dimensional Abelian variety

Abstract

Let be a simple - or -dimensional Abelian variety over the field of complex numbers, where is a prime number. Assume that one of the following conditions holds:1) is a totally real field of degree 1, 2 or 4 over ; 2) is a simple -dimensional Abelian variety of CM-type such that is a normal extension;3) is a simple -dimensional Abelian variety such that is an imaginary quadratic extension of .Then for every positive integer the -space is spanned by cohomology classes of intersections of divisors.