  We derive hamiltionian generators of asymptotic symmetries for general
relativity with asymptotic AdS boundary conditions using the ``covariant phase
space'' method of Wald et al. We then compare our results with other
definitions that have been proposed in the literature. We find that our
definition agrees with that proposed by Ashtekar et al, with the spinor
definition, and with the background dependent definition of Henneaux and
Teitelboim. Our definition disagrees with the one obtained from the
``counterterm subtraction method,'' but the difference is found to consist only
of a ``constant offset'' that is determined entirely in terms of the boundary
metric. We finally discuss and justify our boundary conditions by a linear
perturbation analysis, and we comment on generalizations of our boundary
conditions, as well as inclusion of matter fields.
