The Absolute Anabelian Geometry of Virtual Curves Arising from Sections of Arithmetic Fundamental Groups of Configuration Spaces

Abstract: The objective of this paper is to study the anabelian object referred to as \emph{pointed virtual curves}. Namely, given a family of curves $Y \rightarrow X$ over a field $k$ under suitable conditions, we consider the fundamental-group-theoretic pullback of a Galois section $G_{k} \rightarrow \Pi_{X}$. We show that, in various aspects, such pullbacks exhibit anabelian properties analogous to those of the fundamental group of a curve over $k$.