2013 Fiscal Year Research-status Report
| Project/Area Number |
25400004
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 – 2016-03-31
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| Keywords | mixed Tate motives / Hodge realization / semi-algebraic sets |
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| Research Abstract |
This year we have worked on the construction of the Hodge realization of the category of the mixed Tate motives. The crucial object for this is a certain complex of topological chains TC on the products of the one-dimensional projective
spaces over the field of complex numbers. We have succeeded in the construction of the complex TC using the theory of semi-algebraic sets. The most difficult fact to prove is the convergence of integrals of certain differential forms with logarithmic poles on the elements of TC. The main ingredients to prove this are Hironka's theorem on the resolution of singularities, and Lojasiewicz' inequality on continous semi-algebraic functions on compact semi-algebraic sets.
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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 have succeeded in the construction of the complex TC. Now we are trying to write up a paper.
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| Strategy for Future Research Activity |
Our next project is to generalize our construction of the complex TC to the case of mixed elliptic motives. The reason we needed to carry over some of the grant to next year is, we still need to have some meetings to write up the results.
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| Expenditure Plans for the Next FY Research Funding |
To write up our results, we still need to have some meetings.
I will have some meetings with my collabolator Tomohide Terasoma and Masaki Hanamura.
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