Motivic aspects of anabelian geometry

Abstract

We discuss the role which might be played in anabelian geometry by the étale homotopy type of Artin and Mazur. We quote some results around the question how local the construction is. Furthermore, we show that, after completion away from the residue characteristics, the functor étale homotopy type factors through the motivic $\mathrm{A}^1$-homotopy category of Morel–Voevodsky.