4 problems

Let $U_n=\operatorname{Spec}\left(\mathbb{Z}\left[\frac{1}{n}\right]\right)$ for square-free $n\in\mathbb{N}$, let $\pi_A^t(U_n)$ denote the finite groups appearing as Galois group…

Unramified inverse Galois conjecture. Every finite group $G$ occurs as the Galois group

Let $K$ be a field. A finite group occurs as a Galois group over $K$ if it is isomorphic to the Galois group of a finite Galois extension of $K$. Hilbert's inverse Galois conjectur…

Semi-topological inverse Galois conjecture. There exists a Weierstrass polynomial $f$ on $X$ such that the splitting covering $E_f \stackrel{q}{\rightarrow}X$ is equivalent to the…