Definition 29.4.4 (0C4H)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.4: Closed immersions and quasi-coherent sheaves
Definition 29.4.4 (cite)

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Definition 29.4.4. Let $X$ be a scheme. Let $Z, Y \subset X$ be closed subschemes corresponding to quasi-coherent ideal sheaves $\mathcal{I}, \mathcal{J} \subset \mathcal{O}_ X$ . The scheme theoretic intersection of $Z$ and $Y$ is the closed subscheme of $X$ cut out by $\mathcal{I} + \mathcal{J}$ . The scheme theoretic union of $Z$ and $Y$ is the closed subscheme of $X$ cut out by $\mathcal{I} \cap \mathcal{J}$ .

Comments (2)

Comment #3179 by Jonathan Gruner on February 08, 2018 at 10:19

"Then scheme theoretic union" should be "The scheme theoretic union".

Comment #3292 by Johan on May 16, 2018 at 18:46

Thanks very much. Fixed here.

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