PDE's are geometric objects to which one can associate conservation laws in relation to their symmetry properties . Then, the wholly-cohomological character of a PDE is its possibility to represent any $(n-1)$-dimensional cohomological class of the $n$-dimensional basis manifold by means of a conservation law. In this paper we resume some recent results in this direction obtained by the author and also announce some new further results for PDEs defined in the category of supermanifolds.
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