Mono-anabelian Reconstruction of Number Fields with Restricted Ramification

TL;DR

This paper demonstrates a method to reconstruct number fields and their maximal unramified outside S extensions using group-theoretic techniques based on Hoshi's mono-anabelian reconstruction, starting from the profinite Galois group.

Contribution

It introduces a novel approach to reconstruct number fields and their extensions from profinite groups, extending previous anabelian techniques to a broader class of fields.

Findings

Successful reconstruction of number fields from Galois groups

Extension to maximal unramified outside S extensions for density 1 primes

Advancement in group-theoretic methods for number field reconstruction

Abstract

In this paper, we apply Hoshi's mono-anabelian reconstruction of number fields to establish a group-theoretic reconstruction of a number field K together with its maximal unramified outside S extension K_S for a density 1 subset of primes of K starting from the profinite group G_{K,S}.