Lemma 33.24.2 (04Q0)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 33: Varieties
Section 33.24: Closures of products
Lemma 33.24.2 (cite)

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Lemma 33.24.2. Let $k$ be a field. Let $f : A \to X$ , $g : B \to Y$ be morphisms of schemes over $k$ . Then set theoretically we have

$\overline{f(A)} \times _ k \overline{g(B)} = \overline{(f \times g)(A \times _ k B)}$

Proof. This follows from Lemma 33.24.1 as the image of $f \times g$ is $f(A)g(B)$ in the notation of that lemma. $\square$

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