Covering groups and their integral models
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- by Martin H. Weissman PDF
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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 âintegral modelsâ 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 Gerstenâs conjecture.References
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Additional Information
- Martin H. Weissman
- Affiliation: Division of Science, Yale-NUS College, 16 College Ave West #02-221, Singapore 138527
- MR Author ID: 718173
- Email: marty.weissman@yale-nus.edu.sg
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 3695-3725
- MSC (2010): Primary 14L99, 19C09
- DOI: https://doi.org/10.1090/tran/6598
- MathSciNet review: 3451891