Chow group

Summary

The Chow groups of a variety $X$ are the groups of algebraic cycles on $X$ modulo rational equivalence, one for each dimension. They are the algebraic analogue of homology groups. For a smooth variety, the intersection product turns their sum into a graded ring, the Chow ring, which is the setting of intersection theory. In codimension one they recover the divisor class group and the Picard group of a smooth variety.