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Bulletin of the London Mathematical Society (1)

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ON COVERINGS OF DELIGNE–MUMFORD STACKS AND SURJECTIVITY OF THE BRAUER MAP
ANDREW KRESCH, ANGELO VISTOLI
Journal:

Bulletin of the London Mathematical Society / Volume 36 / Issue 2 / March 2004

Published online by Cambridge University Press:

02 February 2004, pp. 188-192

Print publication:

March 2004
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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.Research of the first author supported in part by the Wolfgang Paul program of the Humboldt Foundation; research of the second author supported in part by the University of Bologna, funds for selected research topics.