A note on highly Kummer-faithful fields

2020/05/28 by Yoshiyasu Ozeki, Ozeki, Yoshiyasu, Yuichiro Taguchi +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2005.13721

openalex publication_date 2020/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of highly Kummer-faithful fields and study its relationship with the notion of Kummer-faithful fields. We also give some examples of highly Kummer-faithful fields. For example, if k is a number field of finite degree over ℚ, g is an integer >0 and m=(m_p)_p is a family of non-negative integers, where p ranges over all prime numbers, then the extension field k_g,m obtained by adjoining to k all coordinates of the elements of the p^m_p-torsion subgroup A[p^m_p] of A for all semi-abelian varieties A over k of dimension at most g and all prime numbers p, is highly Kummer-faithful.

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