| 研究課題/領域番号 |
21K13765
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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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| 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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| 次年度使用額が生じた理由 |
I plan to participate in various international conferences, and visit researchers abroad to pursue my research (the details of these business trips are not yet finalized). I also plan to purchase a Windows computer to use for my research (the software that I use is not compatible with Mac).
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