The Stacks project

Lemma 66.4.12. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Consider the map

\[ \{ \mathop{\mathrm{Spec}}(k) \to X \text{ monomorphism where }k\text{ is a field}\} \longrightarrow |X| \]

This map is injective.

Proof. This follows from Lemma 66.4.11. $\square$

Comments (2)

Comment #7758 by Laurent Moret-Bailly on

In connection with Comment #7747, what is really proved here is this: if is a monomorphism, then every defining the same point factors (uniquely) through . The stated result follows immediately.

There are also:

  • 4 comment(s) on Section 66.4: Points of algebraic spaces

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