  The Bisognano-Wichmann property on the geometric behavior of the modular
group of the von Neumann algebras of local observables associated to wedge
regions in Quantum Field Theory is shown to provide an intrinsic sufficient
criterion for the existence of a covariant action of the (universal covering
of) the Poincar\'e group. In particular this gives, together with our previous
results, an intrinsic characterization of positive-energy conformal
pre-cosheaves of von Neumann algebras. To this end we adapt to our use Moore
theory of central extensions of locally compact groups by polish groups,
selecting and making an analysis of a wider class of extensions with natural
measurable properties and showing henceforth that the universal covering of the
Poincar\'e group has only trivial central extensions (vanishing of the first
and second order cohomology) within our class.
