 An "r"-cycle is a formal sum of closed integral subschemes of "X" whose relative dimension is "r"; here the relative dimension of formula_25 is the transcendence degree of formula_26 over formula_27 minus the codimension of formula_28 in "S".Rational equivalence can also be replaced by several other coarser equivalence relations on algebraic cycles.Other equivalence relations of interest include "algebraic equivalence", "homological equivalence" for a fixed cohomology theory (such as singular cohomology or étale cohomology), "numerical equivalence", as well as all of the above modulo torsion.