2017 Fiscal Year Research-status Report
| Project/Area Number |
15K04793
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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) |
2015-04-01 – 2019-03-31
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| Keywords | Iwasawa / function fields / abelian variety |
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| Outline of Annual Research Achievements |
We have obtained results concerning the Geometric Iwasawa Main conjecture in two cases:1) semistable abelian varieties and unramified everywhere p-adic Lie extensions.2)semistable abelian varieties and finite etale extensions. These two results prove the full Geometric Iwasawa Main Conjecture under these assumptions. We hope to generalize our results to general abelian varieties and ramifying extensions. Both papers have received referee reports and we are making the suitable corrections now. A third project is on the way: U operator on the space of oververconvergent Drinfeld modular forms. (Joint work with Prof. Nicole)
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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
We proved already two cases of our main Conjecture and hope to extend our results further on
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| Strategy for Future Research Activity |
We hope to generalize our results to general abelian varieties and ramifying extensions as well as work on the new project with Prof. Nicole.
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| Causes of Carryover |
During the academic year 2017-18 I had heavy teaching duties that did not allow me to travel or consacre so much time to research.
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Research Products
(3 results)
