global problems on non-commutative algebraic geometry
| Project/Area Number |
24540044
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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 | Kochi University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
松澤 淳一 奈良女子大学, 自然科学系, 教授 (00212217)
石井 亮 広島大学, 理学研究科, 教授 (10252420)
吉冨 賢太郎 大阪府立大学, 公私立大学の部局等, 准教授 (10305609)
菊地 克彦 京都大学, 理学研究科, 助教 (50283586)
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| Co-Investigator(Renkei-kenkyūsha) |
Mochizuki Takuro 京都大学, 数理解析研究所, 教授 (10315971)
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 非可換代数幾何学 / 非可換環論 / ワイル環 / ジャコビアン問題 / 非可換代数多様体 / 非可換射影多様体 / ドルボー複体 / Deligne-Illusie 理論 / 非可換ケーラー多様体 / ケーラー多様体 / 非可換幾何学 / 射影多様体 / 力学系 / 有限体 / ゼータ関数 / Jacobian 問題 / Dixmier 予想 / 多項式力学系 |
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| Outline of Final Research Achievements |
Regarding non-commutative algebraic geometry, we can apply ordinary algebraic geometry method by understanding through reduction to the positive characteristics. We organized the geometric problems, raised one way of thinking about the definition itself and regularity of non-commutative varieties.
I defined the non-commutative projective space and a version of the theory of differential forms on it, and set the pathway of calculating its cohomology.
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Report
(6 results)
Research Products
(50 results)
