Example 62.5.2. Let $f : X \to S$ be a morphism of schemes which is locally of finite type. Let $r \geq 0$ be an integer. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module of finite type. For $s \in S$ denote $\mathcal{F}_ s$ the pullback of $\mathcal{F}$ to $X_ s$. Assume $\dim (\text{Supp}(\mathcal{F}_ s)) \leq r$ for all $s \in S$. Then we can associate to $\mathcal{F}$ the family $[\mathcal{F}/X/S]_ r$ of $r$-cycles on fibres of $X/S$ defined by the formula

where $[\mathcal{F}_ s]_ r$ is given by Chow Homology, Definition 42.10.2.

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