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Absolute noetherian approximation of algebraic stacks

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arxiv 2311.09208 v1 pith:EZP3ME7S submitted 2023-11-15 math.AG

David Rydh This is my paper · ORCID
classification math.AG
keywords algebraicnoetherianstackabsoluteapplicationsapproximatedapproximationeliminating
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We show that every quasi-compact and quasi-separated algebraic stack can be approximated by a noetherian algebraic stack. We give several applications such as eliminating noetherian hypotheses in the theory of good moduli spaces.

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  1. Compact approximation and descent for algebraic stacks

    math.AG 2025-04 conditional novelty 6.0 of 10

    Approximation by compact complexes holds for quasi-compact quasi-separated algebraic stacks with quasi-finite diagonal, and this property descends along quasi-finite flat covers.

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