From the Introduction: The purpose of this Appendix is to prove a technical part of Bogomolov’s program in anabelian geometry, concerning recovering the nature of the base field, given enough information from the local theory. In broad terms, if $v$ is a quasi-divisorial valuation, and thus the residue field of $v$ is a function field over an algebraically closed base field, the question of determining the nature of the base field asks whether or not this base field is the algebraic closure of a finite field.