Lemma 64.22.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\overline{x}$ be a geometric point of $X$. Let $(U, \overline{u})$ be an étale neighbourhood of $\overline{x}$ where $U$ is a scheme. Then we have

where the left hand side is the stalk of the structure sheaf of $X$, and the right hand side is the strict henselization of the local ring of $U$ at the point $u$ at which $\overline{u}$ is centered.

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