| Project/Area Number |
21K13765
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Saitama University |
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Principal Investigator |
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| Project Period (FY) |
2021-04-01 – 2026-03-31
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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2025: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2024: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2023: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 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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| Outline of Research at the Start |
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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| Outline of Annual Research Achievements |
- 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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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
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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| Strategy for Future Research Activity |
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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