Abstract
In this article we investigate homological aspects of a skew complete intersection R, i.e. a skew polynomial ring modulo an ideal generated by a sequence of regular normal elements. We compute the derived braided Hochschild cohomology of R relative to the skew polynomial ring and show its action on ExtR(M,N) is noetherian for finitely generated R-modules M and N respecting the braiding of R. When the parameters defining the skew polynomial ring are roots of unity we use this action to define a support theory. In this setting applications include a proof of the Generalized Auslander-Reiten Conjecture and that R possesses symmetric complexity.
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