and Anabelian Geometry

October 27 Wednesday, 10:00--11:00 | |

K. Wickelgren
(Harvard University)
Etale pi_1 obstructions to rational points
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Grothendieck's anabelian conjectures say that hyperbolic algebraic curves over number fields should behave like K(pi,1)'s in algebraic geometry. For instance, conjecturally the rational points on such a curve are the sections of etale pi_1 of the structure map. We use cohomological obstructions of Jordan Ellenberg coming from the lower central series of the etale fundamental group to study such sections. We give a complete calculation of the two and three nilpotent local mod 2 obstructions for P^1-{0,1,infty}. Globally, we give a characterization in terms of splitting varieties. This is tantamount to computing the splitting variety of a Massey product in Galois cohomology, which was done jointly with M. Hopkins. Over R, we show a 2-nilpotent section conjecture. |