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Generalization of Koszul cohomology for wedge product with a fixed q-form: literature and references?

Let $A$ be a commutative ring. For an odd positive integer $q$ and an integer $p$ in the range $1 \leq p \leq q$, consider the cochain complex: $0 \to \Lambda^p(A^N) \to \Lambda^{p+q}(A^N) \to \cdots \...
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