2021 Fiscal Year Research-status Report
Class number formula over global field of characteristic p and with coefficients.
| Project/Area Number |
21K03186
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| Research Institution | Sophia University |
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Principal Investigator |
TRIHAN FABIEN 上智大学, 理工学部, 准教授 (60738300)
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| Project Period (FY) |
2021-04-01 – 2026-03-31
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| Keywords | Number theory |
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| Outline of Annual Research Achievements |
During the fiscal year 2021-22, due to the covid situation it was difficult to invite or visit my co-author however, I was able to complete the revision of my paper “ A comparison theorem for semi-abelian schemes over a smooth curve.” with D. Vauclair as well as “ On the μ-invariants of abelian varieties over function fields of characteristic p>0” with my co-authors Lai,Longhi,Suzuki and Tan, both accepted for publication. In February 2022 I have visited the University of Rennes and had fruitful conversation with Prof. Gros about my on-going project on the Tamagawa Number conjecture with coefficients. Later on that same month, I attended a conference on Motives in Milan, followed by a 10 days stay at the University of Padova, host of Prof. Chiarellotto, an expert in the field of p-advice coefficients. I had also the opportunity there to give a talk on the topic. Since March 2022, I am the guest of Prof. Kakde, IISc Bangalore who is a world reknown expert on Iwasawa Main conjecture, including cases in the function field case.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
During 10 of the 12 months, the borders were closed due to the covid situation. It was impossible to travel and impossible to invite my co-authors. Of course, you can use ZOOM or other software, but there is nothing better than the face to face meetings to do research
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| Strategy for Future Research Activity |
The project has been a bit delayed but my objectives remain the same: to establish a Tamagawa Number formula in characteristic p that will generalize the one of Milne-Ramachandran. Also, it appears that further work toward the calculation of mu-invariant of abelian varieties can be done. Namely we plan with Prof. Tan to establish new results in the case of ramified extension of function fields. This is another aspect of the research that I would like to develop in the future.
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| Causes of Carryover |
Due to the covid19 pandemic, the border of Japan were basically closed until February 2022. Still, at this time it is very difficult for visitor to enter Japan. As a consequence, scientific exchange have been slowed down. I am now starting to travel and thanks to a sabbatical year, I will be able to do so until september 2022 and gather as many travels and scientific collaborations that I can. Also, I hope that the border of Japan will reopen and that I will be able to spend part of the unused amount of my grant during 2021-22 to this academic year 2022-23 by inviting my collaborators.
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