研究課題/領域番号 |
25400004
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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 – 2017-03-31
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キーワード | Hodge realization / mixed Tate motives / semi-algebraic sets |
研究実績の概要 |
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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現在までの達成度 (区分) |
現在までの達成度 (区分)
3: やや遅れている
理由
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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今後の研究の推進方策 |
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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次年度使用額が生じた理由 |
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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次年度使用額の使用計画 |
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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