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RELATIVE COMPLETIONS AND THE COHOMOLOGY OF LINEAR GROUPS OVER LOCAL RINGS

Published online by Cambridge University Press:  06 March 2002

KEVIN P. KNUDSON
Affiliation:
Department of Mathematics, 1150 F/AB, Wayne State University, Detroit, MI 48202, USA; [email protected]
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Abstract

For a discrete group G there are two well known completions. The first is the Malcev (or unipotent) completion. This is a prounipotent group [Uscr ], defined over ℚ, together with a homomorphism ψ : G → [Uscr ] that is universal among maps from G into prounipotent ℚ-groups. To construct [Uscr ], it suffices for us to consider the case where G is nilpotent; the general case is handled by taking the inverse limit of the Malcev completions of the GrG, where Γ[bull ]G denotes the lower central series of G. If G is abelian, then [Uscr ] = G [otimes ] ℚ. We review this construction in Section 2.

Type
Research Article
Copyright
2002 London Mathematical Society

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