  We show that when the Wald-Zoupas prescription is implemented, the resulting
charges realize the BMS symmetry algebra without any 2-cocycle nor central
extension, at any cut of future null infinity. We refine the covariance
prescription for application to the charge aspects, and introduce a new aspect
for Geroch's super-momentum with better covariance properties. For the extended
BMS symmetry with singular conformal Killing vectors we find that a Wald-Zoupas
symplectic potential exists, if one is willing to modify the symplectic
structure by a corner term. The resulting algebra of Noether currents between
two arbitrary cuts is center-less. The charge algebra at a given cut has a
residual field-dependent 2-cocycle, but time-independent and non-radiative.
More precisely, super-rotation fluxes act covariantly, but super-rotation
charges act covariantly only on global translations. The take home message is
that in any situation where 2-cocycles appears in the literature, covariance
has likely been lost in the charge prescription, and that the criterium of
covariance is a powerful one to reduce ambiguities in the charges, and can be
used also for ambiguities in the charge aspects.
