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In noncommutative projective geometry, there is a counterpart of dualizing complex in commutative world. It seems to me that they are called either a balanced dualizing complex or rigid dualizing complex. I am aware that they are different objects but cannot really understand how they are different. I would appreciate it if someone kindly explain to me the difference.

P.S. I am reading this paper by M. van den Bergh

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