The Stacks project

Definition 62.8.1. 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 $X/S$ effective if $\alpha _ s$ is an effective cycle (Chow Homology, Definition 42.8.4) for all $s \in S$. The monoid of all effective relative $r$-cycles on $X/S$ is denoted $z^{eff}(X/S, r)$.