The Stacks project

Definition 62.9.1. 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 $X/S$ is a proper relative cycle if the support of $\alpha $ (Remark 62.5.6) is contained in a closed subset $W \subset X$ proper over $S$ (Cohomology of Schemes, Definition 30.26.2). The group of all proper relative $r$-cycles on $X/S$ is denoted $c(X/S, r)$.

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