Lemma 42.38.7 (0B7H)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 42: Chow Homology and Chern Classes
Section 42.38: Intersecting with Chern classes
Lemma 42.38.7 (cite)

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Lemma 42.38.7. Let $(S, \delta )$ be as in Situation 42.7.1. Let $X$ be locally of finite type over $S$ . Let $\mathcal{E}$ be a locally free $\mathcal{O}_ X$ -module of rank $r$ . Let $0 \leq p \leq r$ . Then the rule that to $f : X' \to X$ assigns $c_ p(f^*\mathcal{E}) \cap - : \mathop{\mathrm{CH}}\nolimits _ k(X') \to \mathop{\mathrm{CH}}\nolimits _{k - p}(X')$ is a bivariant class of degree $p$ .

Proof. Immediate from Lemmas 42.38.3, 42.38.4, 42.38.5, and 42.38.6 and Definition 42.33.1. $\square$

Comments (2)

Comment #5453 by R on August 06, 2020 at 19:54

Typo: "assignes" $\to$ "assigns".

Comment #5672 by Johan on November 14, 2020 at 21:49

Thanks and fixed here.

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