2014 Fiscal Year Research-status Report
| Project/Area Number |
25400004
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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) |
2013-04-01 – 2017-03-31
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| Keywords | Hodge realization |
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| Outline of Annual Research Achievements |
This year we continued on the construction of the Hodge realization of Bloch-Kriz mixed Tate motives. We finished the construction of the chain complex TC last year, but we ovelooked a certain property about the face map which the complex TC should have. We spent sometime to prove that property. Also to show that our construction coincides with the original Hodge realization due to Bloch and Kriz, we need to construct another complex which contains both TC and the complex of somooth differenatial forms with logarithmic poles along the divisor at infinity. Terasoma has got an idea about how to construct such a complex, and we have been working out the details. We decided write a paper on the results we have obtained so far.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
More time was needed than we had expected to prove the necessary properties of the complex TC.
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| Strategy for Future Research Activity |
We will finish the construction of the Hodge realization of mixed Tate motives, and consider the case of mixed elliptic motives.
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| Causes of Carryover |
The progress is a little delayed than our original plan which is to construct the Hodge realization of mixed elliptic motives.
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| Expenditure Plan for Carryover Budget |
Next year we will finish our program for this year. The rest of the badget for this year will be used for this.
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