Abstract
In an author's joint work with Hoshi and Mochizuki, we introduced the notion of TKND-AVKF-field [concerning the divisible subgroups of the groups of rational points of semi-abelian varieties] and obtained an anabelian Grothendieck Conjecture-type result for higher dimensional configuration spaces associated to hyperbolic curves over TKND-AVKF-fields. On the other hand, every concrete example of TKND-AVKF-field that appears in this joint work is a $\times\mu$-indivisible field [i.e., a field such that any divisible element of the multiplicative group of the field is a root of unity]. In the present paper, we construct new examples of TKND-AVKF-fields that are not $\times\mu$-indivisible.
Acknowledgment
The author would like to thank Professor Ivan Fesenko for asking questions concerning the contents of [2] that stimulate the author to write the present paper. The author also would like to thank Professor Shinichi Mochizuki for a helpful discussion concerning the contents of the present paper. Moreover, the author also would like to thank the referee for reading carefully and giving the author several suggestions. This research was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
Citation
Shota Tsujimura. "Construction of Non-$\times\mu$-Indivisible TKND-AVKF-fields." Kodai Math. J. 45 (1) 38 - 48, March 2022. https://doi.org/10.2996/kmj/kmj45103
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