论文标题
相对Cohen-Macaulay模块的二元性和等效性
Dualities and equivalences of the category of relative Cohen-Macaulay modules
论文作者
论文摘要
在本文中，我们通过开发相对Cohen-Macaulay模块的理论来建立局部代数中一些二元性和等价的全球类似物。让r成为具有身份的通勤性noetherian环（不一定是局部）。引入了A相关双重化模块的概念和与A相关的大型Cohen-Macaulay模块。借助A相关二元模块，我们建立了二元性的全球类似物，该类似于本地代数中Cohen-Macaulay模块的子类别。最后，我们研究了A-Relative Cohen-Macaulay模块的子类别和A-Relative广义的Cohen-Macaulay模块的行为。
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.
