2021 Fiscal Year Final Research Report
Algebraic cycles and motives with modulus for unipotent algebraic groups
| Project/Area Number |
16K17579
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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 | Japan Women's University (2018-2021)
Tokyo Denki University (2016-2017) |
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Principal Investigator |
SUGIYAMA Rin 日本女子大学, 理学部, 講師 (20633233)
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| Project Period (FY) |
2016-04-01 – 2022-03-31
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| Keywords | 相互層 / 加法群のテンソル積 / モジュラス付き代数的サイクル |
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| Outline of Final Research Achievements |
Tensor structures of reciprocity sheaves induced by tensor structures on the category of modulus sheaves with transfers were revealed. Using this I computed concretely the tensor products of the additive groups and the multiplicative groups as reciprocity sheaves. In particular, I computed the tensor product of two copies of the additive group. This is a completely new result, since the theory of motive using the homotopy invariance can not deal with that case.I also gave a description of the Chow group of 0-cycles with modulus for product of curves in terms of the tensor product of its Jacobian varieties.
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| Free Research Field |
数論幾何
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| Academic Significance and Societal Importance of the Research Achievements |
代数多様体のモチーフに関する理論は盛んに研究され続けている理論であり、その中でホモトピー不変性を仮定しないモチーフ理論（モジュラス付きモチーフの理論）は近年発展しているものである。今回の研究成果は、ホモトピー不変でない最も基本的な対象である加法群について、新たな枠組みでの計算を行い、その構造を明らかにした。今後も関連する計算は、モジュラス付きモチーフの振る舞いを明らかにすることへ繋がると思われる。
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