In this talk I will explain how to recognize complex tori among Kähler klt spaces (smooth in codimension 2) in terms of vanishing of Chern numbers. It requires first to define Chern classes on singular spaces (a rather unstable notion). On the way, we will establish a singular version of the Bogomolov-Gieseker inequality for stable sheaves and study what can be said in the equality case. Joint work with Patrick Graf and Henri Guenancia.