Summary: Asymptotically anti-de Sitter spacetimes are considered in a general dimension \(d\geq 4\). As one might expect, the boundary conditions at infinity ensure that the asymptotic symmetry group is the anti-de Sitter group (although there is an interesting subtlety if \(d=4\)). Asymptotic field equations imply that, associated with each generator \(\xi\) of this group, there is a quantity \(Q_\xi\) which satisfies the expected ‘balance equation’ if there is a flux of physical matter fields across the boundary \({\mathcal I}\) at infinity and is absolutely conserved in the absence of this flux. Irrespective of the dimension \(d\), all of these quantities vanish if the spacetime under considerations is (globally) anti-de Sitter. Furthermore, this result is required by a general covariance argument. However, it contradicts some of the recent findings based on the conjectured AdS/CFT duality. This and other features of our analysis suggest that, if a consistent dictionary between gravity und conformal field theories does exist in fully non-perturbative regimes, it would have to be more subtle than the one used currently.