Study on the properties on local cohomology modules from view points of wide cohomology theories
| Project/Area Number |
23540048
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nara University of Education |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
HANAKI Ryo 奈良教育大学, 教育学部, 准教授 (70549162)
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| Co-Investigator(Renkei-kenkyūsha) |
ETO Kazufumi 日本工業大学, 工学部, 教授 (30271357)
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| Research Collaborator |
中平 豊 奈良教育大学, 大学院
中村 力 奈良教育大学, 大学院
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 局所コホモロジー / 余有限加群 / 双対性 / 自己準同型環 / 代数学 / 数学教育 / グラフ理論 / モノミアル / 局所コホモロジー加群 / 圏 / 余有限 / 可換代数 / バス数 / 代数幾何 / 余有限複体 / 幾何学 / 組紐理論 |
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| Research Abstract |
In the period with the grant, we proved that the category M(R, J)cof of J-cofinite modules is a full sub-category abelian category of the category of all R-modules, provided the ideal J is principal up to radical, where J is an ideal of a noetherian ring R. Further we could give a characterization over regular rings complete with respect to a J-adic topology, after Hartshorne, on the question: when is the complex bounded below J-cofinite?
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Report
(4 results)
Research Products
(47 results)
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[Presentation] 単項イデアルに関する余有限加群の圏について2012
Author(s)
川崎 謙一郎 (奈良教育大), 重光裕至 (奈良教育大)
Organizer
Workshop on Commutative Algebra 2012 in Nara University of Education ~ Cohomology theory and Related topics ~
Place of Presentation
奈良教育大学 新館 2 号棟 R5-212
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[Presentation] 使える教材の工夫2010
Author(s)
川崎 謙一郎
Organizer
淡路中学校教育研究会数学部会研究会, 第I会場
Place of Presentation
南あわじ市立南淡中学校
Year and Date
2010-11-19
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