%0 Journal Article
%T Hodge classes on abelian varieties of low dimension
%A B. J. J. Moonen
%A Yu. G. Zarhin
%J Mathematics
%D 1999
%I arXiv
%X In this paper we study Hodge classes on complex abelian varieties. We prove some general results that allow us, in certain cases, to compute the Hodge group of a product abelian variety $X = X_1 \times X_2$ once we know the Hodge groups of the two factors. Using these results we can compute the Hodge groups of all abelian varieties of dimension $\leq 5$. We prove that the Hodge ring of any such abelian variety $X$ is generated by divisor classes together with the so-called Weil classes on (quotients of) $X$.
%U http://arxiv.org/abs/math/9901113v2