 Chow group

The Chow group is $A_k(X)=Z_k(X)/{\mathrm{Rat}}_k(X)$, the group of $k$-dimensional algebraic cycles modulo rational equivalence.

The Chow group is a fundamental concept in algebraic geometry and is used to study algebraic cycles on algebraic varieties. It plays a crucial role in intersection theory, the study of the intersection properties of algebraic cycles, and in the formulation of various cohomological theories.