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Grothendieck's Section Conjecture and zero-cycles on varieties

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If you have a question about this talk, please contact Mustapha Amrani.

Non-Abelian Fundamental Groups in Arithmetic Geometry

After some background material on Grothendieck’s Section Conjecture, we discuss an obstruction for the existence of splittings of the abelianized homotopy exact sequence for the tale fundamental group. As an application, we explain how to find examples for smooth projective curves over Q that have points everywhere locally but the homotopy exact sequence does not split. This is joint work with David Harari, with explicit examples contributed by Victor Flynn.

This talk is part of the Isaac Newton Institute Seminar Series series.

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