Dualities and equivalences of the category of relative Cohen-Macaulay modules
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2022
- DOI:
- 10.48550/arXiv.2210.08551
- arXiv:
- arXiv:2210.08551
- Bibcode:
- 2022arXiv221008551P
- Keywords:
-
- Mathematics - Commutative Algebra;
- 13C14;
- 13D07;
- 13D45;
- 13D09
- E-Print:
- to appear in the Journal of Commutative Algebra