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15 July 2008 Cohomological goodness and the profinite completion of Bianchi groups
F. Grunewald, A. Jaikin-Zapirain, P. A. Zalesskii
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Duke Math. J. 144(1): 53-72 (15 July 2008). DOI: 10.1215/00127094-2008-031

Abstract

The concept of cohomological goodness was introduced by J.-P. Serre in his book on Galois cohomology [31]. This property relates the cohomology groups of a group to those of its profinite completion. We develop properties of goodness and establish goodness for certain important groups. We prove, for example, that the Bianchi groups (i.e., the groups PSL(2,O), where O is the ring of integers in an imaginary quadratic number field) are good. As an application of our improved understanding of goodness, we are able to show that certain natural central extensions of Fuchsian groups are residually finite. This result contrasts with examples of P. Deligne [5], who shows that the analogous central extensions of Sp(4,Z) do not have this property

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F. Grunewald. A. Jaikin-Zapirain. P. A. Zalesskii. "Cohomological goodness and the profinite completion of Bianchi groups." Duke Math. J. 144 (1) 53 - 72, 15 July 2008. https://doi.org/10.1215/00127094-2008-031

Information

Published: 15 July 2008
First available in Project Euclid: 2 July 2008

zbMATH: 1194.20029
MathSciNet: MR2429321
Digital Object Identifier: 10.1215/00127094-2008-031

Subjects:
Primary: 11F75 , 20H05
Secondary: 14G32 , 19B37 , 57N10

Rights: Copyright © 2008 Duke University Press

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