Construction of Non-×μ-Indivisible TKND-AVKF-Fields

Abstract

In an author's joint work with Hoshi and Mochizuki, we introduced the notion of TKND-AVKF- fields [concerning the divisible subgroups of the groups of rationalpoints of semi-abelian varieties] and obtained an anabelian Grothendieck Conjecture-type result for higher dimensional con guration spaces associated to hyperbolic curvesover TKND-AVKF- fields. On the other hand, every concrete example of TKND-AVKF-fields. that appears in this joint work is a ×μ-indivisible eld [i.e., a eld such that anydivisible element of the multiplicative group of the eld is a root of unity]. In the presentpaper, we construct new examples of TKND-AVKF-fields that are not ×μ-indivisible.