2012 Fiscal Year Final Research Report
Studies of Cohen-Macaulay modules over Gorenstein local rings
| Project/Area Number |
22740008
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Nagoya University (2011-2012)
Shinshu University (2010) |
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Principal Investigator |
TAKAHASHI Ryo 名古屋大学, 多元数理科学研究科, 准教授 (40447719)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 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 |
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| Research Abstract |
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.
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Research Products
(63 results)
