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The Stacks project

Lemma 101.18.3. Let \mathcal{X} be an algebraic stack. We have

\mathcal{X}_{\text{ft-pts}} = \bigcup \nolimits _{\varphi : U \to \mathcal{X}\text{ smooth}} |\varphi |(U_0)

where U_0 is the set of closed points of U. Here we may let U range over all schemes smooth over \mathcal{X} or over all affine schemes smooth over \mathcal{X}.

Proof. Immediate from Lemma 101.18.1. \square

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