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

2023/07/15 by Alberto Corato, Corato, Alberto, Mohamed Saı̈di +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2307.07834

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

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