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 |
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 |
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 (2022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 |
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 |
Building up on previous work with my coauthors Naoki Imai (Tokyo University) and Wushi Goldring (Stockholm University), we completed three preprints in 2022. In those papers, we show instances of a general conjecture regarding the weight of automorphic forms in characteristic p. We also prove certain vanishing results for the cohomology of Shimura varieties, which improves on results from previous papers. We have submitted our preprints in peer-reviewed journals.
I presented this research at a conference in Niseko in September 2022. I was also invited to a Oberwokfach workshop on the arithmetic of Shimura varieties, where I discussed my research with several mathematicians, and planned on future research projects.
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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
Together with my coauthors, we made good progress on several problems, resulting in the completion of three different papers. We also found new interesting problems to investigate in our future research.
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今後の研究の推進方策 |
We plan to continue working on the "weight conjecture" for Hodge-type Shimura varieties. Recently, we showed several instances of this conjecture for several low-dimensional Shimura varieties. Also, in the case of unitary Shimura varieties of signature (n-1,1), we proved a weak version. In the future, we would like to extand our results to all unitary Shimura varieties, and eventually to all Hodge-type Shimura varieties. I plan to take part in several conferences to connect with researchers and extand my network.
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