Lemma 66.11.4. Let $S$ be a scheme. Let $X$ be a decent algebraic space over $S$. For every point $x \in |X|$ there exists an étale morphism

where $U$ is an affine scheme, $u$ is the only point of $U$ lying over $x$, and the induced homomorphism $\kappa (x) \to \kappa (u)$ is an isomorphism.

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