The 3rd MSJ-SI

The Mathematical Society of Japan, Seasonal Institute

Development of Galois-Teichmüller Theory
and Anabelian Geometry

October 27 Wednesday, 10:00--11:00
K. Wickelgren (Harvard University)
Etale pi_1 obstructions to rational points
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.