### Grothendieck's Section Conjecture and zero-cycles on varieties

Szamuely, T *(Renyi Institute)*

Monday 27 July 2009, 14:00-15:00

Seminar Room 1, Newton Institute

#### Abstract

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 étale 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.

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