On proper coverings of Artin stacks

By Martin Olsson. 2005

107 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d818e8f51726936dbe5b1a1a7c19d303372e2a78

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Local Systems on Proper Algebraic V -manifolds (2010, methodology): “This is equivalent to the existence of a surjective covering map from a proper scheme [63] [81] [46].”
Remarks on the stack of coherent algebras (2006, methodology): “The algebraic approximation of formal deformations is accomplished using the Grothendieck Existence Theorem for Artin stacks proven by Olsson [11].”
Thom-Sebastiani & Duality for Matrix Factorizations (2011, background): “X) →IndDCoh(π0X) is conservative by Lemma 2.5.2, we may reduce to the case of X and X′ = Specπ0A discrete and in particular ordinary separated stacks. Since π0A is Noetherian, Chow’s Lemma for stacks [O1] shows that X′ receives a proper surjection from a projective π0A-scheme. Thus, it suﬃces to pro”
Families of rationally simply connected varieties over surfaces and torsors for semisimple groups (2008, background): “gne-Mumford, because automorphism group schemes are reduced. Finally, to see 3 note that M g,I(Y/S,β) is quasi-compact in this case by the argument in [Kon95, page 338]. Thus it is proper over S, see [Ols05] and [Fal03, Appendix] to see why. By [KM97] the coarse moduli space exists, and by the above”
Coherent Tannaka duality and algebraicity of Hom-stacks (2014, background): “y assume that S is an aﬃne integral scheme. By Corollary C.5, we may in addition assume that Z →S has geometrically normal ﬁbers. Let W →Z be a proper surjective morphism with W a projective S-scheme [Ols05]. By replacing S with a dense open, we may assume that W →S is ﬂat. By Proposition C.7, we ma”
Noetherian approximation of algebraic spaces and stacks (2009, unknown): “β Sαβ of noetherian aﬃne schemes, we can, by Proposition (B.2), assume that fα is the pull-back of a ﬁnitely presented separated morphism Xαβ →Sαβ. Then, by Chow’s lemma [Knu71, Ch. IV, Thm. 3.1] and [Ols05], there exists a scheme Zαβ and a proper surjective morphism Zαβ →Xαβ. Let Zα = Zαβ ×S αβ Sα.”
Hom-stacks and restriction of scalars (2006, background): “Since R̂ is noetherian, this implies that there exists an integer r ≥ 1 such that S ⊂ Spec(R̂/JrbR) as desired.”