2013 Fiscal Year Final Research Report
Study on triangulated categories and its application to Cohen-Macaulay modules
| Project/Area Number |
21340008
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Okayama University |
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Principal Investigator |
YOSHINO Yuji 岡山大学, 自然科学研究科, 教授 (00135302)
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| Co-Investigator(Kenkyū-buntansha) |
ARAYA Tokuji 岡山理科大学, 理学部, 准教授 (70613222)
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| Co-Investigator(Renkei-kenkyūsha) |
IYAMA Osamu 名古屋大学, 大学院・多元数理科学研究科, 教授 (70347532)
TAKAHASHI Ryo 名古屋大学, 大学院・多元数理科学研究科, 准教授 (40447719)
YAMAGATA Kunio 東京農工大学, 共生科学技術研究科, 教授 (60015849)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 代数学 / 可換環 / Cohen-Macaulay加群 / 導来圏 / 安定圏 / 退化 |
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| Research Abstract |
In order to analyze the degeneration of Cohen-Macaulay modules, we have given careful consideration to the analogue of degeneration in the stable category, which we call the stable degeneration. As a result we obtained several satisfactory results which clarify the degeneration over a simple singularity.
Moreover, about a finitely generated module over a complete local ring of prime characteristic, we gave a proof of the duality theorem between the left Frobenius actions on a module and the right Frobenius actions on its Matlis dual module.
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[Presentation] Local cohomology and t-structure2010
Author(s)
Yuji Yoshino
Organizer
The 5th Japan-Vietnam joint seminar on commutative algebra
Place of Presentation
Vietnam Academy of Science and Technology, Institute of Mathematics, Hanoi, Vietnam
Year and Date
20100105-09
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