Studies of Cohen-Macaulay modules over Gorenstein local rings

Gorenstein 局部环上的 Cohen-Macaulay 模的研究

• 批准号: 22740008
• 负责人: TAKAHASHI Ryo
• 金额: $ 2.66万
• 依托单位: Nagoya University (2011-2012)Shinshu University (2010)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740008/
• 关键词: Gorenstein 環; Cohen-Macaulay 環; Cohen-Macaulay 加群; 加群圏; 導来圏; 特異圏; 分解部分圏; thick 部分圏; 可換Noether環; resolving部分圏; thick部分圏; Cohen-Macaulay環; 三角次元; 三角圏; 次元; 有界導来圏; Gorenstein環; Cohen-Macaulay加群; 安定圏; Cohen-Macaulay; 特殊化閉; 超曲面; Gorenstein

The structure of Cohen-Macaulay modules that are locally free on the punctured spectrum was investigated, and a result of Keller, Murfet and Van den Bergh on Cohen-Macaulay modules over the completion was recovered. The resolving subcategories of Cohen-Macaulay modules over a hypersurface and the thick subcategories of the singularity category were classified completely by using specialization closed subsets of the singular locus. As an application, a theorem of Huneke and Wiegand on the rigidity of Tor modules was recovered.

研究了穿孔谱上局部自由的 Cohen-Macaulay 模块的结构，并恢复了 Keller、Murfet 和 Van den Bergh 对完井时 Cohen-Macaulay 模块的结果。利用奇异轨迹的特化封闭子集对超曲面上的科恩-麦考利模块的解析子类和奇点类别的厚子类进行了完全分类。作为应用，恢复了 Huneke 和 Wiegand 关于 Tor 模块刚性的定理。

项目成果

Homological aspects of semidualizing modules

半二元化模块的同源方面

• 发表时间: 2010
• 影响因子: 0.5
• 作者: Ryo Takahashi;Diana White
• 通讯作者: Diana White

Uniform annihilation of Ext modules and generation of derived categories

统一消灭Ext模块并生成派生类别

• 发表时间: 2013
• 作者: Ryo Takahashi

Classifying resolving subcategories by grade consistent functions

按等级一致功能对解析子类别进行分类

• 发表时间: 2012
• 作者: Ryo Takahashi

Gorensteinホモロジー代数入門

Gorenstein 同调代数导论

• 发表时间: 2012
• 作者: 高橋亮

Finiteness of dimensions of resolving subcategories

解析子类别的维数有限性

• 发表时间: 2011
• 作者: Ryo Takahashi