On copies of the absolute Galois group in $\operatorname {Out}F_2$
On copies of the absolute Galois group in $\operatorname {Out}F_2$
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 …