Definition 101.8.1 (0510)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 101: Morphisms of Algebraic Stacks
Section 101.8: Noetherian algebraic stacks
Definition 101.8.1 (cite)

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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 September 11, 2022 at 03:13

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 $\ref{http://www.math.uchicago.edu/~emerton/pdffiles/formal-stacks.pdf}$ even for formal algebraic stacks, but I just want to see what happens in the special case of algebraic stacks.)

Comment #7996 by Stacks Project on January 14, 2023 at 12:39

Not sure what you're asking.

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