A research on properties on local cohomology modules from the approach of category theory.
| Project/Area Number |
26400044
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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(Renkei-kenkyūsha) |
Eto Kazufumi 日本工業大学, 工学部, 教授 (30271357)
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| Research Collaborator |
Tsurii Tatsuya 大阪府立大学, 客員研究員
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 代数学 / 可換代数 / 局所コホモロジー加群 / 圏(アーベル圏,セール圏) / 余有限加群 / モノミアル / ハイパー群 / 算数・数学教育 / 圏(セール圏, アーベル圏, etc) / 圏(セール圏, アーベル圏) / 余有限複体 / 双対性 / 導来圏 / 数学教育 |
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| Outline of Final Research Achievements |
The chief researcher obained the following assertion and its proof in detail during the period supported by the grant:
Theorem. Let A be a homomorphic image of a Gorenstein ring of finite Krull dimension, J an ideal of A of dimension one, and N* a bounded-below complex of A-modules. Suppose that A is complete with respect to a J-adic topology. During the preriod supported by the grant, we could give a proof that N・ is a J -cofinite complex if and only if Hi(N・)is a J-cofinite module for all i. The same result is also proved for principal ideals J. Consequently, for the fourth question given by R. Hartshorne, we obtain an answer over the ring, on affine curves and hypersurfaces.
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Report
(4 results)
Research Products
(9 results)
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[Presentation] `一般化された局所コホモロジー加群の余有限性について'2014
Author(s)
Ken-ichiroh Kawasaki
Organizer
Workshop on Commutative Algebra 2014 II in Nara University of Education
Place of Presentation
Room No. R5-212, in the 2nd floor of New Building No. 2, Place: Nara University of Education.
Year and Date
2014-05-30
Related Report
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