Definition 100.18.2. Let $\mathcal{X}$ be an algebraic stack. We say a point $x \in |\mathcal{X}|$ is a finite type point1 if the equivalent conditions of Lemma 100.18.1 are satisfied. We denote $\mathcal{X}_{\text{ft-pts}}$ the set of finite type points of $\mathcal{X}$.

[1] This is a slight abuse of language as it would perhaps be more correct to say “locally finite type point”.

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