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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