  Boundary charges in gauge theories (like the ADM mass in general relativity)
can be understood as integrals of linear conserved n-2 forms of the free theory
obtained by linearization around the background. These forms are associated
one-to-one to reducibility parameters of this background (like the time-like
Killing vector of Minkowski space-time). In this paper, closed n-2 forms in the
full interacting theory are constructed in terms of a one parameter family of
solutions to the full equations of motion that admits a reducibility parameter.
These forms thus allow one to apply Stokes theorem without bulk contributions
and, provided appropriate fall-off conditions are satisfied, they reduce
asymptotically near the boundary to the conserved n-2 forms of the linearized
theory. As an application, the first law of black hole mechanics in
asymptotically anti-de Sitter space-times is derived.
