On copies of the absolute Galois group in $\mathrm{Out}{\hat{F}}_2$

Abstract

In this article we consider outer Galois actions on a free profinite group of rank two, induced by the étale fundamental group of a projective line minus three points or of a pointed elliptic curve over a number field. Under mild technical assumptions their respective images uniquely determine the curves and the number fields.

9 pages. This replaces the older version "Galois actions on higher dessins d'enfants", with substantial changes

Cited by in corpus (1)

• The Galois action on Hurwitz curves