Definition 26.4.1. Let i : Z \to X be a morphism of locally ringed spaces. We say that i is a closed immersion if:
The map i is a homeomorphism of Z onto a closed subset of X.
The map \mathcal{O}_ X \to i_*\mathcal{O}_ Z is surjective; let \mathcal{I} denote the kernel.
The \mathcal{O}_ X-module \mathcal{I} is locally generated by sections.
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