2015 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 / mixed Tate motives / semi-algebraic sets |
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| Outline of Annual Research Achievements |
This year we have succeeded in the construction of the Hodge realization functor on the category of mixed Tate motives. Although the basic idea was obtained some time ago, there have been several technical difficulties.
Introducing the theory of semi-algebraic sets was the crucial step in overcoming the difficulties. The most remarkable fact is that we have shown that one can calculate the Hodge realization of any mixed Tate motive in terms of period integrals of logarithmic differential forms on products of projective lines.
We have written two papers on this subject. Now they are on arXiv math; arXiv:1604.03216 and arXiv:1509.06950.
Next year we plan to go to the construction of the Hodge realization of mixed elliptic motives.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
We had planned to finish the construction of the Hodge realization of the category of mixed elliptic motives this year. this will be postponed to the next year.
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| Strategy for Future Research Activity |
We will construct the Hodge realization of the category of mixed elliptic motives.
There are some differences from the case of mixed Tate motives, but we should be able to deal this case too.
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| Causes of Carryover |
We had planned to finish the construction of the Hodge realization of the mixed elliptic motives, but it took us longer to finish the case of mixed Tate motives. This will be postponed to the next year.
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| Expenditure Plan for Carryover Budget |
Together with Terasoma and Hanamura we will finish the construction of the Hodge realization of the mixed elliptic motives. we need travel expenses. We plan to have a workshop on this subject.
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