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 $\mathcal{I} \cap \mathcal{J}$.

Comment #3179 by Jonathan Gruner on

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

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