Let $U$ be an open subscheme of $\textrm{Spec} \ \mathbf{Z}$. The complement of $U$ is a divisor $D$ of $\textrm{Spec} \ \mathbf{Z}$.

Q. Can we classify the etale coverings of $U$ of a given degree?

Given a finite etale morphism $\pi:V\longrightarrow U$, the normalization of $X$ in the function field $L$ of $V$ is $\textrm{Spec} \ O_L$. Can we also say what $V$ itself should be?

Of course, we can complicate things by replacing $\textrm{Spec} \ \mathbf{Z}$ by $\textrm{Spec} \ O_K$.

Example. Take $U= \textrm{Spec} \ \mathbf{Z} -\{ (2)\}$ and let $V\rightarrow U$ be an finite etale morphism. Suppose that $V$ is connected and that let $K$ be its function field. The normalization of $\textrm{Spec} \ \mathbf{Z}$ in $K$ is of course $O_K$. The extension $\mathbf{Z}\subset O_K$ is unramified outside $(2)$ and (possibly) ramified at $(2)$. Can one give a description of $V$ here?

EDIT. I just realized one can also ask themselves a similar question for $\mathbf{P}^1_{\mathbf{C}}$. Or even better, for any Riemann surface $X$.