Profinite structures interpretable in fields

We investigate profinite structures in the sense of Newelski interpretable in fields. We show that profinite structures interpretable in separably closed fields are the same as profinite structures weakly interpretable in ACF p . We also find a strong connection with the inverse Galois problem. e field theoretic constructions of profinite structures weakly interpretable in ACF p and satisfying some model theoretic properties, like smallness, m -normality, non-triviality, being M -rank 1. For example we interpret in this way the profinite structure consisting of the profinite group Z p ω together with a distinguished Sylow p -subgroup of its standard structural group.