Lemma 82.26.4. In Situation 82.2.1 let $X/B$ be good. Let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module. Then the rule that to $f : X' \to X$ assigns $c_1(f^*\mathcal{L}) \cap - : \mathop{\mathrm{CH}}\nolimits _ k(X') \to \mathop{\mathrm{CH}}\nolimits _{k - 1}(X')$ is a bivariant class of degree $1$.

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