**DIPS 1/98**[tex source, PostScript, PDF file, dvi]-
**Title:**COHOMOLOGY BACKGROUND IN GEOMETRY OF PDE**Author:**Joseph KRASIL'SHCHIKUsing techniques of Fr\"olicher\,--\,Nijenhuis brackets, we associate to any formally integrable equation $\CC{E}$ a cohomology theory ($\CC{C}$-complex) $H_\CC{C}^*(\CC{E})$ related to deformations of the equation structure on the infinite prolongation $\Ei$. A subgroup in $H_\CC{C}^1(\CC{E})$ is identified with recursion operators acting on the Lie algebra $\sym\CC{E}$ of symmetries. On the other hand, another subgroup of $H_\CC{C}^*(\CC{E})$ can be understood as the algebra of supersymmetries of the ``superization'' of the equation $\CC{E}$. This pass to superequations makes it possible to obtain a well-defined action of recursion operators in nonlocal setting. Relations to Poisson structures on $\Ei$ are briefly discussed.

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