The m-step Solvable Mono-anabelian Geometry of Number Fields

2025/11/07 by Yu Mao, Mao, Yu, Mohamed Saı̈di +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2511.05192

openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28

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 ≥ 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.

Citations

• The m-step solvable anabelian geometry of number fields

Cited by

• The 6-step Solvable Mono-anabelian Reconstruction of Abelian Number Fields

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