2017 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 | Hodge realization |
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| Outline of Annual Research Achievements |
In the construction of the Hodge realization of mixed Tate motives, we defined so ca-lled admissible chain complexes. We expect that this complex can be used to de-scribe the Abel-Jacobi map of higher Chow groups and have started working on it-s proof. This can be used to identify the Hodge realization of certain mixed Tate mo-tives e.g. that Polylogarithms with the regulator of certain higher Chow groups.
Other project we started with Tomohide Terasoma is to clarify the construction of
the mixed elliptic motives, and define the Hodge realization of it. For this we ne-ed to modify the construction of the case of mixed Tate motives.
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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
So far our strategy seems to be the correct one.
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| Strategy for Future Research Activity |
Our method should work for motives of finite dimensions. Very recently Ayoub announced the proof of the conservativity conjecture. If this is correct, all motives are finite dimensional, and our method can be applied very widely.
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| Causes of Carryover |
I needed to postpone a business travel for some personal reasons. Next year I will use the travel money as had been planned.
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