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2023 Fiscal Year Research-status Report

Geometry of Shimura varieties in positive characteristic

Research Project

Project/Area Number 21K13765
Research InstitutionSaitama University

Principal Investigator

Koskivirta Jean・Stefan  埼玉大学, 理工学研究科, 准教授 (00897613)

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

- 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".

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.

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.

Causes of Carryover

I plan to use the grant in the next fiscal year, as I will be making several research trips to Europe (Gothenburg University, King's College London, Caen University).

  • Research Products

    (2 results)

All 2023

All Presentation (2 results) (of which Int'l Joint Research: 2 results,  Invited: 2 results)

  • [Presentation] Shimura Varieties and G-zips2023

    • Author(s)
      Jean-Stefan Koskivirta
    • Organizer
      Number Theory Seminar, Caen University
    • Int'l Joint Research / Invited
  • [Presentation] Weights of mod p automorphic forms2023

    • Author(s)
      Jean-Stefan Koskivirta
    • Organizer
      Number Theory Seminar, Caen University
    • Int'l Joint Research / Invited

URL: 

Published: 2024-12-25  

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