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arXiv · 0904.0227

Noetherian approximation of algebraic spaces and stacks

David Rydh
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Abstract

We show that every scheme/algebraic space/stack that is quasi-compact with quasi-finite diagonal can be approximated by a noetherian scheme/algebraic space/stack. More generally, we show that any stack which is etale-locally a global quotient stack can be approximated. Examples of applications are generalizations of Chevalley's, Serre's and Zariski's theorems and Chow's lemma to the non-noetherian setting. We also show that every quasi-compact algebraic stack with quasi-finite diagonal has a finite generically flat cover by a scheme.

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BibTeXRIS

David Rydh. 2014-09-18. Noetherian approximation of algebraic spaces and stacks. https://doi.org/10.1016/j.jalgebra.2014.09.012

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