The no-interpretable-fields conjecture for torsion-free hyperbolic groups

Let $G$ be a torsion-free hyperbolic group. An interpretable field is a field interpretable in a model of $Th(G)$. No-interpretable-fields conjecture. No infinite field is interpretable in any model of $Th(G)$. This conjecture concerns the structure of interpretable sets in models of theories of torsion-free hyperbolic groups; the paper proves related results, including that the generic type of a non-cyclic torsion-free hyperbolic group is foreign to any interpretable abelian group, hence also to any interpretable field.