Covering groups and their integral models

Weissman, Martin

doi:10.1090/tran/6598

Covering groups and their integral models
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by Martin H. Weissman PDF

Trans. Amer. Math. Soc. 368 (2016), 3695-3725 Request permission

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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