Definition 68.11.7. Let $S$ be a scheme. Let $X$ be a decent algebraic space over $S$. Let $x \in |X|$. The *henselian local ring of $X$ at $x$*, is

\[ \mathcal{O}_{X, x}^ h = \mathop{\mathrm{colim}}\nolimits \Gamma (U, \mathcal{O}_ U) \]

where the colimit is over the elementary étale neighbourhoods $(U, u) \to (X, x)$.

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