Recovering function fields from their decomposition graphs

Abstract

We develop the global theory of a strategy to tackle a program initiated by Bogomolov in 1990. That program aims at giving a group-theoretical recipe by which one can reconstruct function fields K | k with td(K | k) > 1 and k algebraically closed from the maximal pro-abelian-by-central Galois group Π Kc of K, where is any prime number ≠char(k).