A Chow group is the Abelian group of algebraic cycles of a fixed dimension modulo rational
equivalence. For a complex algebraic variety 
, the group 
consists of finite integer
combinations of closed points, with relations given
by divisors of rational functions on integral
curves in 
.
For a proper connected algebraic variety, the
degree homomorphism sums the coefficients, and its kernel is denoted 
.
For a smooth variety, the groups graded by codimension form the Chow ring under the intersection product. Bloch's conjecture for surfaces concerns the information about zero-cycles retained by degree and the Albanese homomorphism.
