Situation 76.56.1. Let $S$ be a scheme. Let $X$ be a quasi-compact and quasi-separated algebraic space over $S$. Let $V \to X$ be a surjective étale morphism where $V$ is an affine scheme (such a thing exists by Properties of Spaces, Lemma 66.6.3). Choose a commutative diagram
\[ \xymatrix{ V \ar[rd]_\varphi \ar[rr]_ j & & Y \ar[ld]^\pi \\ & X } \]
where $j$ is an open immersion and $\pi $ is a finite morphism of algebraic spaces (such a diagram exists by Lemma 76.34.3). Let $\mathcal{I} \subset \mathcal{O}_ Y$ be a finite type quasi-coherent sheaf of ideals on $Y$ with $V(\mathcal{I}) = Y \setminus j(V)$ (such a sheaf of ideals exists by Limits of Spaces, Lemma 70.14.1).
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