Algebraic cycle

Summary

An algebraic cycle on a variety $X$ is a finite formal sum, with integer coefficients, of irreducible closed subvarieties of $X$. Cycles of codimension one are the Weil divisors. Cycles modulo rational equivalence form the Chow groups, the basic objects of intersection theory. The question of which cohomology classes come from cycles is the subject of the Hodge conjecture and of the standard conjectures.