The Stacks project

Example 42.33.7. Let $(S, \delta )$ be as in Situation 42.7.1. Let $X$ be locally of finite type over $S$. Let $(\mathcal{L}, s, i : D \to X)$ a triple as in Definition 42.29.1. Let $Z \to X$ be a morphism of schemes locally of finite type and let $c \in A^ p(Z \to X)$ be a bivariant class. Then the bivariant gysin class $c' \in A^1(D \to X)$ of Lemma 42.33.3 commutes with $c$ in the sense of Remark 42.33.6. Namely, this is a restatement of condition (3) of Definition 42.33.1.