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Noetherian approximation of algebraic spaces and stacks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2505-6417
2015 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 422, 105-147 p.Article in journal (Refereed) Published
Abstract [en]

We show that every scheme (resp. algebraic space, resp. algebraic stack) that is quasi-compact with quasi-finite diagonal can be approximated by a noetherian scheme (resp. algebraic space, resp. 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.

Place, publisher, year, edition, pages
2015. Vol. 422, 105-147 p.
Keyword [en]
Noetherian approximation, Algebraic spaces, Algebraic stacks, Chevalley's theorem, Serre's theorem, Global quotient stacks, Global type, Basic stacks
National Category
Algebra and Logic
URN: urn:nbn:se:kth:diva-158793DOI: 10.1016/j.jalgebra.2014.09.012ISI: 000345058300007ScopusID: 2-s2.0-84908607554OAI: diva2:787907

QC 20150212

Available from: 2015-02-12 Created: 2015-01-12 Last updated: 2015-02-12Bibliographically approved

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Rydh, David
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