University of Cambridge > Talks.cam > Algebraic Geometry Seminar > Profinite completions, curvature, and decision problems

Profinite completions, curvature, and decision problems

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  • UserMartin Bridson (Oxford)
  • ClockWednesday 16 November 2011, 14:15-15:15
  • HouseMR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

In 1970 Grothendieck asked: if G_1 and G_2 are finitely presented, residually finite groups, and there is a map between them that induces an isomorphism of profinite completions, must the original map be an isomorphism? Fritz Grunewald and I showed that the answer is “no”. Our solution opens up a rich array of possibilities around the questions: how different can G_1 and G_2 be? and what additional hypotheses force G_1 to be isomorphic to G_2? I shall describe recent progress on these questions, explaining in particular how dramatically the algorithmic complexity of G_1 and G_2 can differ.

This talk is part of the Algebraic Geometry Seminar series.

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