研究課題/領域番号 |
18K03258
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研究種目 |
基盤研究(C)
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配分区分 | 基金 |
応募区分 | 一般 |
審査区分 |
小区分11010:代数学関連
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研究機関 | 立教大学 |
研究代表者 |
ガイサ トーマス 立教大学, 理学部, 教授 (30571963)
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研究期間 (年度) |
2018-04-01 – 2024-03-31
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研究課題ステータス |
交付 (2022年度)
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配分額 *注記 |
4,290千円 (直接経費: 3,300千円、間接経費: 990千円)
2022年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2021年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2020年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2019年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2018年度: 1,040千円 (直接経費: 800千円、間接経費: 240千円)
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キーワード | Weil etale cohomology / Local class field theory / Duality / Locally compact groups / One-motives / Birch Swinnerton Dyer / Brauer group / Weil-etale cohomology / Tamagawa number formula / BSD conjecture / Brauer Manin obstruction / Arithmetic cohomology / Class field theory / cohomology theory / local fields |
研究実績の概要 |
In my ongoing project on Weil-etale cohomology for schemes over henselian discrete valuation rings, finite fields, and arithmetic schemes, I was able to finalize publication of the following results: Joint with B.Morin, we outline the definition of a Weil-etale cohomology theory for varieties over local fields which satisfy a Pontrjagin duality theory. The groups are objects of the heart of the t-structure on the derived category of locally compact abelian groups (this work is accepted for publication and published online). As an application we prove results on class field theory over local fields, generalizing and improving work of S.Saito and Yoshida. We give an integral model for the fundamental group, and some extra information on the kernel of the reciprocity map (a preprint is submitted for publication). In joint work with T.Suzuki, we generalized our work on the Weil-etale version of the Birch and Swinnerton-Dyer conjecture to one-motives. In particular, our work gives a new proof of the Tamagawa number formula of Oda (this is published).
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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
The work was slightly delayed due to the corona measures, and the project had to continue into an extra year.
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今後の研究の推進方策 |
It is the last year of the project and it only remains to publish the last remaining preprint, to survey the results we obtained, and to attend conferences to present my results.
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