# Moscow Mathematical Journal

Volume 17, Issue 3, July–September 2017 pp. 371–383.

On a Generalization of the Neukirch–Uchida Theorem

**Authors**:
Alexander B. Ivanov (1)

**Author institution:**(1) Technische Universität München, Zentrum Mathematik-M11, Boltzmannstr. 3, 85748 Garching bei München

**Summary: **

In this article we generalize a part of Neukirch–Uchida theorem for number fields from the birational case to the case of curves
Spec 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 ε > 0 in the tower *K _{S}*/

*K*.

2010 Math. Subj. Class. 11R34, 11R37, 14G32.

**Keywords:**Number fields, anabelian geometry, Neukirch–Uchida theorem, densities of primes, stable sets of primes.

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