Lemma 42.33.3 (0B79)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 42: Chow Homology and Chern Classes
Section 42.33: Bivariant intersection theory
Lemma 42.33.3 (cite)

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Lemma 42.33.3. Let $(S, \delta )$ be as in Situation 42.7.1. Let $X$ be locally of finite type over $S$ . Let $(\mathcal{L}, s, i : D \to X)$ be a triple as in Definition 42.29.1. Then the rule that to $f : X' \to X$ assigns $(i')^* : \mathop{\mathrm{CH}}\nolimits _ k(X') \to \mathop{\mathrm{CH}}\nolimits _{k - 1}(D')$ where $D' = D \times _ X X'$ is a bivariant class of degree $1$ .

Proof. This follows from Lemmas 42.30.2, 42.29.8, 42.29.9, and 42.30.5. $\square$

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