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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 292, Pages 224–254
DOI: https://doi.org/10.1134/S0371968516010143
(Mi tm3689)
 

This article is cited in 5 scientific papers (total in 5 papers)

On the congruence kernel for simple algebraic groups

Gopal Prasada, Andrei S. Rapinchukb

a Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA
b Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA
Full-text PDF (445 kB) Citations (5)
References:
Abstract: This paper contains several results about the structure of the congruence kernel $C^{(S)}(G)$ of an absolutely almost simple simply connected algebraic group $G$ over a global field $K$ with respect to a set of places $S$ of $K$. In particular, we show that $C^{(S)}(G)$ is always trivial if $S$ contains a generalized arithmetic progression. We also give a criterion for the centrality of $C^{(S)}(G)$ in the general situation in terms of the existence of commuting lifts of the groups $G(K_v)$ for $v\notin S$ in the $S$-arithmetic completion $\widehat {G}^{(S)}$. This result enables one to give simple proofs of the centrality in a number of cases. Finally, we show that if $K$ is a number field and $G$ is $K$-isotropic, then $C^{(S)}(G)$ as a normal subgroup of $\widehat {G}^{(S)}$ is almost generated by a single element.
Funding agency Grant number
National Science Foundation DMS-1401380
DMS-1301800
Both authors were supported by the NSF (grants DMS-1401380 and DMS-1301800).
Received: January 11, 2015
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 292, Pages 216–246
DOI: https://doi.org/10.1134/S0081543816010144
Bibliographic databases:
Document Type: Article
UDC: 512.74
Language: English
Citation: Gopal Prasad, Andrei S. Rapinchuk, “On the congruence kernel for simple algebraic groups”, Algebra, geometry, and number theory, Collected papers. Dedicated to Academician Vladimir Petrovich Platonov on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 292, MAIK Nauka/Interperiodica, Moscow, 2016, 224–254; Proc. Steklov Inst. Math., 292 (2016), 216–246
Citation in format AMSBIB
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\bookinfo Collected papers. Dedicated to Academician Vladimir Petrovich Platonov on the occasion of his 75th birthday
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\vol 292
\pages 224--254
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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