Title: Dualizing Complexes over Noncommutative Graded Algebras

Publication status: J. Algebra 153 no. 1 (1992), 41-84.

The paper introduces a noncommutative version of Grothendieck Duality Theory. We consider a noncommutative graded algebra A over a field. A dualizing complex over A is, roughly, a complex of bimodules which induces a duality between the derived categories of left and right A-modules. We prove uniqueness of dualizing complexes, and existence is some special cases. Of particular importance is the idea of balanced dualizing complex, which is relates to local duality.

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