English

The m-step Solvable Hom-Form of Birational Anabelian Geometry for Number Fields

Number Theory 2023-07-18 v1

Abstract

In 1981, Uchida proved a conditional version of the Hom-form of the Grothendieck birational anabelian conjecture for number fields. In this paper we prove an m-step solvable conditional version of the Grothendieck birational anabelian conjecture for number fields whereby our conditions are slightly weaker than the ones in Uchida's theorem. Furthermore, as in Uchida's work, we show that our result is unconditional in the case where the number field relating to the domain of the given homomorphism is Q\mathbb{Q}

Keywords

Cite

@article{arxiv.2307.07834,
  title  = {The m-step Solvable Hom-Form of Birational Anabelian Geometry for Number Fields},
  author = {Alberto Corato and Mohamed Saïdi},
  journal= {arXiv preprint arXiv:2307.07834},
  year   = {2023}
}