2016 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 / Geometric / Hida / function |
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| Outline of Annual Research Achievements |
The main achievements of this year 2016 were the completion of the proof of the Iwasawa Main conjecture for abelian varieties over function fields of characteristic p>0 in the following two cases: constant ordinary abelian varieties over finitely ramified abelian extensions and semi stable abelian varieties over unramified p-adic Lie extensions. As a result we were able to publish two papers in international reviews and to submit a third one.
-The following paper was accepted for publication King Fai Lai, Ignazio Longhi, Ki-Seng Tan and Fabien Trihan, Pontryagin duality for Iwasawa modules and abelian varieties, Transactions of the AMS, https://doi.org/10.1090/tran/7016. The following paper was completed and submitted:Fabien Trihan and D. Vauclair, On the Geometric Iwasawa Main Conjecture in the non-commutative case, https://arxiv.org/abs/1702.04620. The following paper Fabien Trihan and D. Vauclair, A comparison theorem for semiabelian schemes over smooth curves, http://arxiv.org/abs/1505.02942 is also in the refereeing process. I started a collaboration with Prof. M-H Nicole on modular forms and Hida family for global fields of characteristic p>0. We hope that this new approach will find applications in the Geoemtric Iwasawa theory
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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
My project on Geometric Iwasawa with prof. Vauclair is progressing smoothly; we are now working on a proof of a case of the Tamagawa Equivariant Conjecture for abelian variety over function fieds of characteristic p.
I initiated a new collaboration with Prof. Nicole on Hida family over function fields
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| Strategy for Future Research Activity |
I plan to pursue my project with Prof. Vauclair and Nicole next academic year.
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| Causes of Carryover |
Due to teaching duties I had to cancel a trip abroad.
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| Expenditure Plan for Carryover Budget |
I will invite Prof Nicole, Boyukduk, Vauclair and will have several trips abroad.
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Research Products
(2 results)
