Lemma 42.67.8. In Situation 42.67.1 let $X \to S$ be locally of finite type and let $X' \to S'$ be the base change by $S' \to S$. Let $\mathcal{E}$ be a finite locally free $\mathcal{O}_ X$-module of rank $r$ with base change $\mathcal{E}'$ on $X'$. Then the diagram

of chow groups commutes for all $i$.

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