The Stacks project

Remark 42.29.6. Let $X \to S$, $\mathcal{L}$, $s$, $i : D \to X$ be as in Definition 42.29.1 and assume that $\mathcal{L}|_ D \cong \mathcal{O}_ D$. In this case we can define a canonical map $i^* : Z_{k + 1}(X) \to Z_ k(D)$ on cycles, by requiring that $i^*[W] = 0$ whenever $W \subset D$ is an integral closed subscheme. The possibility to do this will be useful later on.