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For a sigma model of AKSZ-type, we show that the local BRST cohomology isisomorphic to the cohomology of the target space differential when restrictedto coordinate neighborhoods both in the base and in the target. An analogousresult is shown to hold for the cohomology in the space of functionalmultivectors. Applications of these latter cohomology classes in the context ofthe inverse problem of the calculus of variation for general gauge systems arealso discussed.

A Poincare lemma for sigma models of AKSZ type