2020 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 |
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 – 2022-03-31
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Keywords | Abel-Jacobi map / higher Chow cycle |
Outline of Annual Research Achievements |
This year we studied singular and de Rham cohomology groups of complex varieties. Concretely, We showed that singular cohomology groups of a smooth quasi-projective complex variety U relative to a normal crossing divisor H can be described in terms of admissible semi-algebraic chains which we defined earlier. We also showed that the duality pairing between these cohomology groups and de Rham cohomology groups of the complement of H can be described via integral of smooth forms with compact support on U with logarithmic singularity along H on admissible chains. As an application, we showed that the Abel-Jacobi maps on higher Chow cycles on U can be described via integral of logarithmic forms on admissible chains. In particular we showed that the Hodge realization of polylog cycles is equal to a certain Abel-Jacobi image.
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Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
多重楕円ポリログの構成を目指しているが、現在までの所十分な進展が得られていない。
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Strategy for Future Research Activity |
多重楕円ポリログを高次Chowサイクルとして構成する事を目指すが、他の方向性も視野に入れる。
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Causes of Carryover |
コロナ禍の影響で予定していた研究打ち合わせや成果発表ができなかった。今後状況が許せばこれらの活動を再開する。
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Research Products
(1 results)