Lemma 100.9.12. Let \mathcal{X} be an algebraic stack. The rule \mathcal{U} \mapsto |\mathcal{U}| defines an inclusion preserving bijection between open substacks of \mathcal{X} and open subsets of |\mathcal{X}|.
Proof. Choose a presentation [U/R] \to \mathcal{X}, see Algebraic Stacks, Lemma 94.16.2. By Lemma 100.9.11 we see that open substacks correspond to R-invariant open subschemes of U. On the other hand Lemmas 100.4.5 and 100.4.7 guarantee these correspond bijectively to open subsets of |\mathcal{X}|. \square
Comments (0)
There are also: