Shafarevich's freeness conjecture for the absolute Galois group of the maximal abelian extension

Let $\mathbb{Q}_{\rm ab}$ denote the maximal abelian extension of $\mathbb{Q}$, and let $G_{\mathbb{Q}_{\rm ab}}$ be its absolute Galois group. Shafarevich's conjecture. The group $G_{\mathbb{Q}_{\rm ab}}$ is a free profinite group. A positive answer to the question whether $\mathbb{Q}_{\rm ab}$ is ample would imply this conjecture via results of Pop. It remains a long-standing open problem.