Support varieties over skew complete intersections via derived braided Hochschild cohomology

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