Let k be a regular ring, and let A, B be essentially finite type k-algebras. For any functor F:D(ModA) x center dot center dot center dot x D(ModA) -> D(ModB) between their derived categories, we define its twist F-!:D(ModA) x center dot center dot center dot x D(ModA) -> D(ModB) with respect to dualizing complexes, generalizing Grothendieck's construction of f(!). We show that relations between functors are preserved between their twists, and deduce that various relations hold between derived Hochschild (co)-homology and the f(!) functor. We also deduce that the set of isomorphism classes of dualizing complexes over a ring (or a scheme) form a group with respect to derived Hochschild cohomology, and that the twisted inverse image functor is a group homomorphism.
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