Study on modules over commutative rings by categorical methods
| Project/Area Number |
26287008
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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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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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥9,880,000 (Direct Cost: ¥7,600,000、Indirect Cost: ¥2,280,000)
Fiscal Year 2018: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2017: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2016: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 導来圏 / 三角圏 / Cohen-Macaulay 加群 / 次数付き微分加群 / 非有界複体 / 安定圏 / シジジー / DG代数とDG加群 / 代数学 / 可換環論 / 鎖複体 |
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| Outline of Final Research Achievements |
New mathematics called homological algebra has been established in the middle of the 20th century and in the process of this establishment, many problems and conjectures have arisen, which remain unsolved yet. Now in this new century, these problems are regarded as in the framework of the categories. The most interesting objective is to study finitely generated modules over commutative rings that are given by finitely many elements with finitely many relations. However, in this study, we consider the problems once in larger categories called unbounded derived categories that naturally involve infinitely generated modules. Eventually through these methods, we succeeded in deriving several results for finitely generated modules.
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| Academic Significance and Societal Importance of the Research Achievements |
数学の基礎研究であるので特に社会的意義を主張するには及ばない。しかしながら学術的には、半世紀以上未解決であった代数学の問題に対して、それを解決するための糸口が掴めたという点では大きな学術的意義があると考えている。
とくに今回の研究の全般を通して行った導来圏やホモトピー圏などの研究は、問題の解決という意図とは別に、それ自体が数学的に美しい体系を提供しているように思っている。
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Report
(6 results)
Research Products
(19 results)
