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We borrow ideas from Grothendieck duality theory to noncommutative algebra,and use them to prove a reduction result for Hochschild cohomology fornoncommutative algebras which are finite over their center. This generalizes aresult over commutative algebras by Avramov, Iyengar, Lipman and Nayak.

Reduction of Hochschild cohomology over algebras finite over their center