The Stacks project

Lemma 26.13.3. Let $X$ be a scheme. Points of $X$ correspond bijectively to equivalence classes of morphisms from spectra of fields into $X$. Moreover, each equivalence class contains a (unique up to unique isomorphism) smallest element $\mathop{\mathrm{Spec}}(\kappa (x)) \to X$.

Proof. Follows from the discussion above. $\square$

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