Study of subcategories of triangulated categories and derived equivalences of algebras
| Project/Area Number |
22540042
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Tokyo Gakugei University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KURANO Kazuhiko 明治大学, 理工学部, 教授 (90205188)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 環論 / 導来圏 / 三角圏 / ホモトピー圏 / N鎖複体 / 上三角行列環 / 次数環 / 多項式環 / 特異点 / recollement / Iwanaga-Gorenstein環 / Cohen-Macaulay加群 / Cox環 / 標準因子 / stable t-structure / Serre functor / functorially finite部分圏 / Calabi-Yau三角圏 / Seshadri constant / 射影平面 |
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| Research Abstract |
We study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. In the case of the homotopy category of finitely generated projective modules over an Iwanaga-Gorenstein ring, we show the existence of a triangle of recollements in the above quotient category. As an application, we show that this quotient category is triangle equivalent to the stable module category of Cohen-Macaulay T_2(R)-modules.
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Report
(4 results)
Research Products
(7 results)
