The Stacks project

Example 100.11.9. Let $X$ be a scheme and let $x \in X$ be a point. Then the monomorphism $x \to X$ is the residual gerbe of $X$ at $x$ where we, as usual, identify $x$ with the scheme $x = \mathop{\mathrm{Spec}}(\kappa (x))$. If $X$ is an algebraic space and $x \in |X|$, then the residual gerbe at $x$ (which is called the residual space) always exists, see Decent Spaces, Section 68.13.

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