| 研究実績の概要 |
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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