2015 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 Theory / abelian varieties |
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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Our initial objective was to complete the objective 1) with D. Vauclair. We are not completely done because the project is much bigger as we thought (near 200 pages). On the other end, the project with Ki-Seng Tan and others is progressing faster than expected with already two papers accepted for publication in 2016.
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| Strategy for Future Research Activity |
The plan for the next years is 1)Complete the first project wit David Vauclair about comparison between flat and syntomic cohomologies.2) Apply it to the non-commutative Iwasawa main conjecture for abelian varieties over function fields.
3)Finish the project with Tan and others to offer new cases the Iwasawa Main conjecture for abelian varieties over function fields
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| Causes of Carryover |
Some Professors that I wanted to invite declined for this academic year but they assured me that they will come during the next academic year.
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| Expenditure Plan for Carryover Budget |
I will visit my co-authors and will invite them back to Sophia University.
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Research Products
(3 results)
