3 problems

Let $F$ be an infinite field with finitely generated absolute Galois group. Koenigsmann's conjecture. Then $F$ is ample. This conjecture concerns which fields are ample and is pres…

Larsen's conjecture. Then

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…