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Conserved quantities in general relativity and anomalies

Wald's construction of the Noether charge associated with a Killing vector of a solution of a diffeomorphism invariant theory is reviewed. A variation of a solution of the equations of motion is a 1-form on the space of solutions and a symplectic form on the space of solutions is a 2-form. The cohomological nature of the construction is emphasised and this allows conserved quantities to be evaluated without having to go to asymptotic infinity. 
 
The construction gives rise to a double differential complex associated with the exterior derivative on space-time and the exterior derivative on the space of solutions. It is shown that the same double differential complex arises in the discussion of quantum anomalies in gauge theories and gravity.