2021 Fiscal Year Final Research Report
| Project/Area Number |
18K03232
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Keywords | 代数学 / 数論幾何 / 代数幾何学 / 整数論 |
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| Outline of Final Research Achievements |
A category of motives with modulus is constructed. This has been considered as a fundamental goal in this research subject for a decade. The results are published or accepted as a series of three papers. The first is devoted to the theory of modulus pairs and sheaves on them, the second to the sheaf theory on proper modulus pairs, and the third to the construction of the triangulated category of motives with modulus. We have also studied related subjects such as reciprocity sheaves and their tensor product, mixed Hodge structure with modulus, P1-invariant sheaves with transfers, and arithmetic of 1-motives of modular curves.
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| Free Research Field |
代数学
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| Academic Significance and Societal Importance of the Research Achievements |
モジュラス付きモチーフの三角圏は10年以上前からその存在が期待されていたものである．その基盤となる論文が出版されたことは，この分野の研究を推進を促進すると期待される．実際，関連分野で新たな方向の研究を開始した数学者が国内外で（特に若い世代に）現れている．また，Hodge理論における対応物，テンソル積，P1不変層，モジュラー曲線など，関連する話題への応用も与えることができたため，その意義が多くの研究者に伝えられることができると期待している．
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