Lemma 62.9.2 (0H62)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 62: Relative Cycles
Section 62.9: Proper relative cycles
Lemma 62.9.2 (cite)

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Lemma 62.9.2. Let $f : X \to S$ be a morphism of schemes. Assume $S$ is locally Noetherian and $f$ is locally of finite type. Let $r \geq 0$ be an integer. Let $\alpha$ be a relative $r$ -cycle on $X/S$ . If $\alpha$ is proper, then any base change $\alpha$ is proper.

Proof. Omitted. $\square$

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