Geodesic
Grothendieck’s problems concerning profinite completions and representations of groups
Martin R. Bridson1 ; Fritz Grunewald2
1 Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
2 Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
Annals of mathematics, Tome 160 (2004) no. 1, pp. 359-373

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In 1970 Alexander Grothendieck [6] posed the following problem: let $\Gamma_1$ and $\Gamma_2$ be finitely presented, residually finite groups, and let $u:\Gamma_1\to\Gamma_2$ be a homomorphism such that the induced map of profinite completions $\hat u :\hat\Gamma_1\to\hat\Gamma_2$ is an isomorphism; does it follow that $u$ is an isomorphism?

DOI : 10.4007/annals.2004.160.359

Martin R. Bridson 1 ; Fritz Grunewald 2

1 Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
2 Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany 
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Martin R. Bridson; Fritz Grunewald. Grothendieck’s problems concerning profinite completions and representations of groups. Annals of mathematics, Tome 160 (2004) no. 1, pp. 359-373. doi: 10.4007/annals.2004.160.359

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