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On Coverings of Deligne–Mumford Stacks and Surjectivity of the Brauer Map
Author(s) -
Kresch Andrew,
Vistoli Angelo
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002728
Subject(s) - mathematics , moduli space , pure mathematics , affine transformation , brauer group , scheme (mathematics) , class (philosophy) , quotient , space (punctuation) , mathematical analysis , philosophy , artificial intelligence , computer science , linguistics
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).