On Coverings of Deligne–Mumford Stacks and Surjectivity of the Brauer Map

By Andrew Kresch, Angelo Vistoli. 2003

94 citations recorded by the source corpus.

The paper proves a result on the existence of finite flat scheme covers of Deligne–Mumford stacks. This result is used to prove that a large class of smooth Deligne–Mumford stacks with affine moduli space are quotient stacks, and in the case of quasi‐projective moduli space, to reduce the question to a classical question on Brauer groups of schemes. 2000 Mathematics Subject Classification 14A20 (primary), 14F22, 14L30 (secondary).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2843b4bc4660332f249defd61fe67fdddf233493

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Citations in the corpus

Hom-stacks and restriction of scalars (2006, background): “If S is the spectrum of a field and X is a Deligne–Mumford stack which is a global quotient stack and has quasi–projective coarse moduli space, then by ([15], 2.”
Remarks on the stack of coherent algebras (2006, background): “ve coarse moduli space. The connected components of the stack Br Y/S are proper over S. Proof. We can clearly assume that Sis connected. If Sis the spectrum of a ﬁeld, then this follows from the fact [7] that Y admits a ﬁnite ﬂat cover by a projective scheme, combined with 3.3.1. In general we do no”
Moduli of twisted sheaves (2004, methodology): “his question for gerbes is closely related the question of when an arbitrary (tame) Deligne-Mumford stack is a quotient stack. This has been studied by Vistoli, Kresch, Hasset, Edidin and others (see [37], [18], [58] and the references therein). As a consequence of 2.2.2.2, we can rewrite the theory”
Orbifold quantum Riemann–Roch, Lefschetz and Serre (2005, background): “ose Xthat satisfy Assumption 2.5.9. Many interesting stacks, for instance the toric Deligne-Mumford stacks [15], satisfy Assumption 2.5.9. Through the collective eﬀorts of many works, including [29], [53], [27], it is now known that if Xis a smooth, separated, generically tame Deligne-Mumford stack ”
Local Systems on Proper Algebraic V -manifolds (2010, background): “It is a well-known fact that coverings of proper DM-stacks by projective varieties exist [62] [81]:”
Orbifold quasimap theory (2014, background): “(i) Boundedness of Qmapd(C,X): Let (C,x) be a twisted curve and choose a projective 1-dimensional variety C̃ with a degree lC finite flat morphism C̃ → C (see [24]).”