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Grothendieck's problems concerning profinite completions and representations of groups

Abstract:

In 1970 Alexander Grothendieck [6] posed the following problem: let Γ1 and Γ2 be finitely presented, residually finite groups, and let u : Γ1 → Γ2 be a homomorphism such that the induced map of profinite completions û: Γ̂1 → Γ̂2 is an isomorphism; does it follow that u is an isomorphism? In this paper we settle this problem by exhibiting pairs of groups u : P → Γ such that Γ is a direct product of two residually finite, hyperbolic groups, P is a finitely presented subgroup of infinite index, ...

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Publication status:
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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
ANNALS OF MATHEMATICS
Volume:
160
Issue:
1
Pages:
359-373
Publication date:
2004-07-05
ISSN:
0003-486X
URN:
uuid:8adb663c-b378-474e-ac7e-6ab273ac6a11
Source identifiers:
8595
Local pid:
pubs:8595
Language:
English

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