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Obstructions to homotopy sections of curves over number fields

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Non-Abelian Fundamental Groups in Arithmetic Geometry

Grothendieck’s section conjecture is analogous to equivalences between fixed points and homotopy fixed points of Galois actions on related topological spaces. We use cohomological obstructions of Jordan Ellenberg coming from nilpotent approximations to the curve to study the sections of etale pi_1 of the structure map. We will relate Ellenberg’s obstructions to Massey products, and explicitly compute mod 2 versions of the first and second for P^1-{0,1,infty} over Q. Over R, we show the first obstruction alone determines the connected components of real points of the curve from those of the Jacobian.

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

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