Cycles on Abelian varieties

Abstract

For abelian varieties one knows a little more about algebraic cycles than for most other classes of smooth projective varieties. This is mainly due to the fact that the Chow group Ch(X) admits two ring structures, one is induced by the intersection product and the other by the Pontryagin product. The Fourier transform exchanges both ring structures. In this section we give an introduction into the theory of algebraic cycles on abelian varieties.