2018 Fiscal Year Research-status Report
Study of mixed motives by the bar construction
| Project/Area Number |
17K05157
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| Research Institution | University of Tsukuba |
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Principal Investigator |
木村 健一郎 筑波大学, 数理物質系, 講師 (50292496)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | admissible chains |
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| Outline of Annual Research Achievements |
Ths year we worked on an application of the complex of admissible chains we constructed before. Concretely, we gave a new way of describing relative cohomology groups of smooth quasi-projective varieties, and duality pairing of cohomology groups in terms of period integrals. Main ingredients in the proof is Cauchy-Stokes formula generalizing classical Cauchy integral formula to the situation of semi-algebraic chains. As an application, we gave a new description of the Abel-Jacobi map for higher Chow cycles which is a natural generalization of the Abel-Jacobi map for ordinary algebraic cycles defined by Griffiths. An example is the Hodge realization of Polylog cycles defined by Bloch.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
We could make expected progress towards the understanding of realization
of motives. In 2019 we will construct Hodge realization of mixed elliptic
motives.
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| Strategy for Future Research Activity |
We will construct the Hodge realization of the category of mixed elliptic motives,
and will give an explicit description of the Hodge realization of the elliptic polylogarithms.
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| Causes of Carryover |
2018年度は旅費の使用が予定より少額で済んだため残額が生じた。2019度には成果発表のため旅費が必要である。
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