The m-step Solvable Mono-anabelian Geometry of Number Fields
Number Theory
2025-11-10 v1
Abstract
The goal of this paper is to develop a group-theoretic algorithm, to reconstruct a number field (together with its maximal m-step solvable ex- tension for some positive integer m \geq 3) from the maximal m+9-step solv- able quotient of its absolute Galois group. If K is an imaginary quadratic field or Q, we establish a group-theoretic reconstruction algorithm of K from the maximal 6-step solvable quotient of its absolute Galois group.
Keywords
Cite
@article{arxiv.2511.05192,
title = {The m-step Solvable Mono-anabelian Geometry of Number Fields},
author = {Yu Mao and Mohamed Saidi},
journal= {arXiv preprint arXiv:2511.05192},
year = {2025}
}