Introduction to anabelian geometry

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• Alexander Betts (Oxford)
• Friday 11 March 2016, 15:00-16:00
• MR13.

If you have a question about this talk, please contact Christian Lund.

The etale fundamental group of a scheme is a profinite group which simultaneously generalises the notion of the fundamental group of a topological space and the Galois group of a field. As a result, the etale fundamental group sees much of the Diophantine geometry of a scheme, in a sense made precise by Grothendieck’s anabelian conjectures. We will introduce the notion of the etale fundamental group, and its relationship to the Diophantine geometry of curves over number fields. Time permitting, we may also introduce a suitable linearised variant, the de Rham fundamental group, as well as describing how one relativises the definition to S-schemes.

This talk is part of the Junior Geometry Seminar series.

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