Lemma 26.13.3 (01J9)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 26: Schemes
Section 26.13: Points of schemes
Lemma 26.13.3 (cite)

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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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