研究課題/領域番号 |
25400004
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研究種目 |
基盤研究(C)
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研究機関 | 筑波大学 |
研究代表者 |
木村 健一郎 筑波大学, 数理物質系, 講師 (50292496)
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研究期間 (年度) |
2013-04-01 – 2016-03-31
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キーワード | mixed Tate motives / Hodge realization / semi-algebraic sets |
研究概要 |
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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現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
We have succeeded in the construction of the complex TC. Now we are trying to write up a paper.
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今後の研究の推進方策 |
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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次年度の研究費の使用計画 |
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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