| 研究実績の概要 |
1) Concerning:Theorem 1.There exists a canonical Dieudonne crystal D(A) on the log curve (C,Z) extending D(A) such
that the mapping fiber of 1-Frobenius on the crystalline cohomology of D(A) (called syntomic cohomology) can be computed by the flat cohomology of the p-torsion points of A.Me and my co-author met in 2015 and were able to progress in the writing of the paper.A preliminary version of the paper can be found here:http://arxiv.org/abs/1505.029422) For application to non-commutative Iwasawa Main conjecture, we plan to meet again this summer with D. Vauclair.
3) With my other co-authors K.F. Lai, I. Longhi and K.-S. Tan, we have published this year 2016 two new papers:K.F. Lai, I. Longhi, K.-S. Tan , F. Trihan, The Iwasawa Main conjecture of constant ordinary abelian varieties over function fields, to appear in the Proceedings of the London Mathematical Society. K.F. Lai, I. Longhi, K.-S. Tan , F. Trihan, The Iwasawa main conjecture for semistable abelian varieties over function fields, Math. Z. 282 (2016), no. 1-2, 485-510.We are still working on a project on the Pontryagin duality for Iwasawa modules and abelian varieties that we expect to complete this year or the next one.
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