Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank over noetherian rings
Authors:
Andrei S. Rapinchuk and Igor A. Rapinchuk
Journal:
Proc. Amer. Math. Soc. 139 (2011), 30993113
MSC (2010):
Primary 19B37; Secondary 20G35
Published electronically:
January 20, 2011
MathSciNet review:
2811265
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Abstract: Let be a universal ChevalleyDemazure group scheme associated to a reduced irreducible root system of rank For a commutative ring , we let denote the elementary subgroup of the group of points The congruence kernel is then defined to be the kernel of the natural homomorphism where is the profinite completion of and is the congruence completion defined by ideals of finite index. The purpose of this paper is to show that for an arbitrary noetherian ring (with some minor restrictions if is of type or ), the congruence kernel is central in
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Additional Information
Andrei S. Rapinchuk
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
Email:
asr3x@virginia.edu
Igor A. Rapinchuk
Affiliation:
Department of Mathematics, Yale University, New Haven, Connecticut 06502
Email:
igor.rapinchuk@yale.edu
DOI:
http://dx.doi.org/10.1090/S000299392011107366
Received by editor(s):
July 22, 2010
Received by editor(s) in revised form:
August 12, 2010
Published electronically:
January 20, 2011
Communicated by:
Jonathan I. Hall
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
