  In this paper we generalize a part of Neukirch-Uchida theorem for number
fields from the birational case to the case of curves $\Spec \caO_{K,S}$ with
$S$ a stable set of primes of a number field $K$. In particular, such sets can
have arbitrarily small (positive) Dirichlet density. The proof consists of two
parts: first one establishes a local correspondence at the boundary $S$, which
works as in the original proof of Neukirch. But then, in contrast to Neukirchs
proof, a direct conclusion via Chebotarev density theorem is not possible,
since stable sets are in general too small, and one has to use further
arguments.
