2022 Volume 45 Issue 1 Pages 49-64
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 , g is an integer > 0 and m = (mp)p is a family of non-negative integers, where p ranges over all prime numbers, then the extension field kg,m obtained by adjoining to k all coordinates of the elements of the pmp-torsion subgroup A[pmp] 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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