Abstract
Abstract We describe explicitly the Auslander–Reiten translation in the category of bounded complexes of finitely generated maximal Cohen–Macaulay modules, 𝐂b(CM R), over a commutative local Cohen–Macaulay ring R with a canonical module ω. Then the Auslander–Reiten formula is generalized for complexes in 𝐂b(CM R) and we prove the existence theorem of Auslander–Reiten sequences. As an application of our results, we investigate the existence of Auslander–Reiten triangles in the category of perfect complexes as a full triangulated subcategory of 𝐃b(mod R).
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