Further examples of non-geometric sections of arithmetic fundamental groups

Abstract

We show the existence of group-theoretic sections of certain geometrically pro-nilpotent by abelian arithmetic fundamental groups of hyperbolic curves over p-adic local fields which are non-geometric, i.e., which do not arise from rational points. Among these quotients is the geometrically metabelian arithmetic fundamental group.

Accepted for publication in Publications of the Research Institute for Mathematical Sciences. arXiv admin note: text overlap with arXiv:1510.06864