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arXiv · 2210.08551

Dualities and equivalences of the category of relative Cohen-Macaulay modules

Parisa Pourghobadian·Kamran Divaani-Aazar·Ahad Rahimi
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Abstract

In this paper, we establish the global analogues of some dualities and equivalences in local algebra by developing the theory of relative Cohen-Macaulay modules. Let R be a commutative Noetherian ring (not necessarily local) with identity and a a proper ideal of R. The notions of a-relative dualizing modules and a-relative big Cohen-Macaulay modules are introduced. With the help of a-relative dualizing modules, we establish the global analogue of the duality on the subcategory of Cohen-Macaulay modules in local algebra. Lastly, we investigate the behavior of the subcategory of a-relative Cohen-Macaulay modules and a-relative generalized Cohen-Macaulay modules under Foxby equivalence.

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Parisa Pourghobadian, Kamran Divaani-Aazar, Ahad Rahimi. 2022-10-16. Dualities and equivalences of the category of relative Cohen-Macaulay modules. https://arxiv.org/abs/2210.08551

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