| 研究課題/領域番号 |
17K05157
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| 研究機関 | 筑波大学 |
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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) |
2017-04-01 – 2020-03-31
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| キーワード | Hodge realization |
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| 研究実績の概要 |
In the construction of the Hodge realization of mixed Tate motives, we defined so ca-lled admissible chain complexes. We expect that this complex can be used to de-scribe the Abel-Jacobi map of higher Chow groups and have started working on it-s proof. This can be used to identify the Hodge realization of certain mixed Tate mo-tives e.g. that Polylogarithms with the regulator of certain higher Chow groups.
Other project we started with Tomohide Terasoma is to clarify the construction of
the mixed elliptic motives, and define the Hodge realization of it. For this we ne-ed to modify the construction of the case of mixed Tate 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)
2: おおむね順調に進展している
理由
So far our strategy seems to be the correct one.
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| 今後の研究の推進方策 |
Our method should work for motives of finite dimensions. Very recently Ayoub announced the proof of the conservativity conjecture. If this is correct, all motives are finite dimensional, and our method can be applied very widely.
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| 次年度使用額が生じた理由 |
I needed to postpone a business travel for some personal reasons. Next year I will use the travel money as had been planned.
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