2021 Fiscal Year Research-status Report
Geometry of Shimura varieties in positive characteristic
| Project/Area Number |
21K13765
|
|---|
| Research Institution | Saitama University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2021-04-01 – 2026-03-31
|
| Keywords | 志村多様体 / Gジップのスタック / 保型形式 / 簡約群 |
|---|
| Outline of Annual Research Achievements |
In the fiscal year 2021, I published the following paper: "Automorphic vector bundles on the stack of G-Zips (with Naoki Imai), Forum Math. Sigma 9 (2021), Paper No. e37, 31 pp."
I also finished and submitted for publication the following manuscript: "Partial Hasse invariants for Shimura varieties of Hodge-type (with Naoki Imai)."
I also completed two other papers, in collaboration with Naoki Imai and Wushi Goldring, that will be submitted soon for publication.
|
| 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 started several collaborative projects on the topic of automorphic forms on the stack of G-zips, with collaborators Naoki Imai and Wushi Goldring. These projects have materialized into publications, submitted papers and preprints.
|
| Strategy for Future Research Activity |
In the near future, I would like to complete two manuscripts on the topic of automorphic forms in characteristic p in collaboration with Naoki Imai and Wushi Goldring. I expect that we will be able to submit these papers in the course of 2022.
I am also planning to start a new project on the Tate conjecture with Ambrus Pal from Imperial College London.
|
| Causes of Carryover |
I plan to purchase a laptop (16インチMacBook Pro) for research purposes. Also, I am planning a research trip to Niseko for the conference “L-functions and Motives in Niseko 2022".
|
