Abstract:
In this article we generalize a part of Neukirch–Uchida theorem for number fields from the birational case to the case of curves $\operatorname{Spec}\mathcal O_{K,S}$, where $S$ a stable set of primes of a number field $K$. Such sets have positive but arbitrarily small Dirichlet density, which must be uniformly bounded from below by some $\epsilon>0$ in the tower $K_S/K$.
Key words and phrases:number fields, anabelian geometry, Neukirch–Uchida theorem, densities of primes, stable sets of primes.
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