The Stacks project

Definition 68.11.2. Let $S$ be a scheme. Let $X$ be a decent algebraic space over $S$. Let $x \in |X|$. The residue field of $X$ at $x$ is the unique field $\kappa (x)$ which comes equipped with a monomorphism $\mathop{\mathrm{Spec}}(\kappa (x)) \to X$ representing $x$.

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