  We study the UV divergences in the action of the "Wheeler-de Witt patch" in
asymptotically AdS spacetimes, which has been conjectured to be dual to the
computational complexity of the state of the dual field theory on a spatial
slice of the boundary. We show that including a surface term in the action on
the null boundaries which ensures invariance under coordinate transformations
has the additional virtue of removing a stronger than expected divergence,
making the leading divergence proportional to the proper volume of the boundary
spatial slice. We compare the divergences in the action to divergences in the
volume of a maximal spatial slice in the bulk, finding that the qualitative
structure is the same, but subleading divergences have different relative
coefficients in the two cases.
