  For a sigma model of AKSZ-type, we show that the local BRST cohomology is
isomorphic to the cohomology of the target space differential when restricted
to coordinate neighborhoods both in the base and in the target. An analogous
result is shown to hold for the cohomology in the space of functional
multivectors. Applications of these latter cohomology classes in the context of
the inverse problem of the calculus of variation for general gauge systems are
also discussed.
