6 problems

Folk conjecture. For each $n\geq 5$, all but finitely many quadratic number fields admit an unramified extension field of degree $n$ whose normal closure has Galois group $A_n$.

Let $G$ be a finite group, and let $K$ range over quadratic number fields. An extension of $K$ is unramified at all primes when it is unramified at every finite and infinite prime…

Folklore conjecture. For any finite group $G$, there exist infinitely many quadratic number fields $K$ such that $K$ possesses a Galois extension with Galois group $G$ unramified a…

Let $G$ be a finite group. For a number field $K$, let $d(\mathbb{Q},G)$ be the smallest degree $[K:\mathbb{Q}]$ for which $K$ possesses an unramified Galois extension with group…

Let $G$ be a finite group. An unramified $G$-extension is an unramified Galois extension whose Galois group is isomorphic to $G$. Folklore conjecture. For every finite group $G$, u…

Wood's moment conjecture. There exists a number $0<a<1$ such that, for every positive integer $k$,