Noetherian approximation of algebraic spaces and stacks
By David Rydh. 2009
103 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/00acddc7d67b2c75503238183f15f1dd10e96a2d
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Tensor generators on schemes and stacks (2013, background): “Rydh [Ryd13]) allows us to not only eliminate the noetherian hypothesis, but also to rigoursly identify V as a direct limit of vector bundles.”
- Coherent Tannaka duality and algebraicity of Hom-stacks (2014, background): “y of approximation type, but this is currently unknown. It is known, however, that morphisms of algebraic stacks that have quasi-finite and locally separated diagonal are locally of approximation type [Ryd15]. In particular, all quasi-separated morphisms of algebraic stacks that are relatively Delign”
- Hyperdescent and étale K-theory (2019, background): “op. 4.4], there exists a spectral stratification of X such that Y is finite ´etale over each stratum; thus we can reduce to the case where Y is finite ´etale over X. By the “´etale d´evissage” result of [Ryd15] (or the “scallop decomposition” of [Lur18, Sec. 3.4.2]), we can further reduce to the case w”