The Stacks project

Remark 81.7.2. In Situation 81.2.1 let $X/B$ be good. Every $x \in |X|$ can be represented by a (unique) monomorphism $\mathop{\mathrm{Spec}}(k) \to X$ where $k$ is a field, see Decent Spaces, Lemma 67.11.1. Then $k$ is the residue field of $x$ and is denoted $\kappa (x)$. Recall that $X$ has a dense open subscheme $U \subset X$ (Properties of Spaces, Proposition 65.13.3). If $x \in U$, then $\kappa (x)$ agrees with the residue field of $x$ on $U$ as a scheme. See Decent Spaces, Section 67.11.

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