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Covering groups and their integral models


Author: Martin H. Weissman
Journal: Trans. Amer. Math. Soc. 368 (2016), 3695-3725
MSC (2010): Primary 14L99, 19C09
DOI: https://doi.org/10.1090/tran/6598
Published electronically: June 18, 2015
MathSciNet review: 3451891
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Abstract: Given a reductive group $ \mathbf {G}$ over a base scheme $ S$, Brylinski and Deligne studied the central extensions of a reductive group $ \mathbf {G}$ by $ \mathbf {K}_2$, viewing both as sheaves of groups on the big Zariski site over $ S$. Their work classified these extensions by three invariants, for $ S$ the spectrum of a field. We expand upon their work to study ``integral models'' of such central extensions, obtaining similar results for $ S$ the spectrum of a sufficiently nice ring, e.g., a DVR with finite residue field or a DVR containing a field. Milder results are obtained for $ S$ the spectrum of a Dedekind domain, often conditional on Gersten's conjecture.


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Additional Information

Martin H. Weissman
Affiliation: Division of Science, Yale-NUS College, 16 College Ave West #02-221, Singapore 138527
Email: marty.weissman@yale-nus.edu.sg

DOI: https://doi.org/10.1090/tran/6598
Received by editor(s): May 19, 2014
Received by editor(s) in revised form: June 14, 2014, and October 20, 2014
Published electronically: June 18, 2015
Article copyright: © Copyright 2015 American Mathematical Society