2018 Fiscal Year Final Research Report
New perspectives on the singularity theory
| Project/Area Number |
15K17510
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tohoku University (2018)
Osaka University (2015-2017) |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | 特異点 / マッカイ対応 / 整数論 |
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| Outline of Final Research Achievements |
We have obtained new perspectives and theorems about singularities of spaces in positive or mixed characteristics and about roles played by singularities in the number theory. More specifically, we have obtained: (1) perspectives on relation between two conjectures in the number theory, Manin's conjecture and Malle's conjecture, and the role that singularities play there, (2) understanding the structure of wild quotient singularities thanks to development of the wild McKay correspondence, (3) formulation of Vojta's conjecture form the viewpoint of singularities.
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| Free Research Field |
代数幾何
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| Academic Significance and Societal Importance of the Research Achievements |
整数論の代数幾何を用いた研究は数論幾何という大きな分野となっているが、特異点の役割は軽視されてきたように感じられる。本研究により、特異点を通して整数論を見たり、逆に整数論を特異点研究に応用するなどの新しい知見や手法が得られた。また、本研究には一部、数理物理からのアイデアも応用されており、複数分野の境界領域における発展ということができる。
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