Definition 62.7.1. Let $f : X \to S$ be a morphism of schemes. Assume $S$ is locally Noetherian and $f$ is locally of finite type. Let $r \geq 0$ be an integer. We say a relative $r$-cycle $\alpha $ on $X/S$ equidimensional if the support of $\alpha $ (Remark 62.5.6) is contained in a closed subset $W \subset X$ whose relative dimension over $S$ is $\leq r$. The group of all equidimensional relative $r$-cycles on $X/S$ is denoted $z_{equi}(X/S, r)$.
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