| 研究課題/領域番号 |
21K13765
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| 研究種目 |
若手研究
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| 配分区分 | 基金 |
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| 審査区分 |
小区分11010:代数学関連
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| 研究機関 | 埼玉大学 |
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研究代表者 |
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| 研究期間 (年度) |
2021-04-01 – 2026-03-31
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| 研究課題ステータス |
交付 (2023年度)
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| 配分額 *注記 |
4,160千円 (直接経費: 3,200千円、間接経費: 960千円)
2025年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2024年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2023年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2022年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2021年度: 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 | 志村多様体 / Gジップのスタック / 保型形式 / 簡約群 |
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| 研究開始時の研究の概要 |
I intend to use of the stack of G-zips in order to study Shimura varieties in characteristic p, in particularunderstand sections of automorphic vector bundles on Shimura varieties.
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| 研究実績の概要 |
- I was invited at the Oberwolfach workshop in February 2023 on the topic of Shimura varieties, where I exchanged with several researchers.
- I visited a collaborator at Stockholm University to discuss future research in September 2023, and this visit resulted in the start of a new research project.
- I gave two research talks at the University of Caen in September 2023 and visited a collaborator there.
- I submitted three preprints on the arXiv and to research journals. The titles are as follows: (1) "A vanishing theorem for vector-valued Siegel automorphic forms in characteristic p", (2) "Cohomology vanishing for Ekedahl--Oort strata on Hilbert--Blumenthal Shimura varieties" (3) "The stack of G-zips is a Mori dream space". These preprints are a natural continuation of my previous research and constitute considerable progress.
- Following these publications, I have also submitted in early 2024 the following paper: "The cone conjecture for vector-valued Siegel automorphic forms".
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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
I met many new collaborators at conferences and seminars with whom I am currently in contact and working actively on future research projects (Stefan Reppen, Wushi Goldring, Deding Yang, Lorenzo La Porta). In the year 2023, I submitted three new articles (decision on publication still pending), and one other paper in early 2024.
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| 今後の研究の推進方策 |
I have several research projects in progress with new and previous collaborators. I plan to visit some of them at their institution (King's College London, Stockholm University, Tokyo University) to continue this research. Furthermore, I expect that this collaboration will result in several manuscripts that will be made public in the year 2024.
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