Lemma 62.14.2 (0H6S)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 62: Relative Cycles
Section 62.14: Composition of relative cycles
Lemma 62.14.2 (cite)

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Lemma 62.14.2. Let $f : X \to Y$ and $g : Y \to S$ be a morphisms of schemes. Assume $S$ locally Noetherian, $g$ locally of finite type and flat of relative dimension $e \ge 0$ , and $f$ locally of finite type and flat of relative dimension $r \geq 0$ . Then $[X/X/Y]_ r \circ [Y/Y/S]_ e = [X/X/S]_{r + e}$ in $z(X/S, r + e)$ .

Proof. Special case of Lemma 62.13.5. $\square$

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