The Stacks project

Definition 101.8.1. Let $\mathcal{X}$ be an algebraic stack. We say $\mathcal{X}$ is Noetherian if $\mathcal{X}$ is quasi-compact, quasi-separated and locally Noetherian.

Comments (2)

Comment #7750 by DatPham on

Is it written somewhere in the Stacks project a crtierion for an algebraic stack to be Noetherian by using obstruction theory? (Such a crtierion is given in \ref{} even for formal algebraic stacks, but I just want to see what happens in the special case of algebraic stacks.)

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