On the global calculus in local cohomology in BRST theory
  We show that the cohomology groups of the horizontal (total) differential on horizontal (local) exterior forms on the infinite-order jet manifold of an affine bundle coincide with the De Rham cohomology groups of the base manifold. This prevents one from the topological obstruction to the definition of global descent equations in BRST theory on an arbitrary affine bundle. 
G.Giachetta, L.Mangiarotti and G.Sardanashvily