2018 Fiscal Year Annual Research 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 / abelian variety / function field |
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| Outline of Annual Research Achievements |
During the time of our grant we were able to obtain the following results. We have sheafified the syntomic complexes of Kato-Trihan allowing us to make the construction functorial with respect to base change (Joint work with D. Vauclair). As an application, we were able to prove the Iwasawa Main Conjecture for semistable abelian varieties over the arithmetic Zp-extension of a function field of positive characteristic (joint work with K.F Lai, I. Longhi and K.S. Tan). Using the classical conjecture for the trivial motive and some decomposition of the Selmer group of a constant ordinary abelian variety in Frobenius and Vershiebung part, we also proved the Main Conjecture for constant ordinary abelian varieties over a product of Zp extensions ramified at a finite set of places of a function field of positive characteristic (a joint work with K.F Lai, I. Longhi and K.S. Tan). We have also treated the case of the Iwasawa Main Conjecture for semistable abelian varieties over unramified p-adic Lie extension of a function field of positive characteristic. Finally, some cases of the Equivariant Tamagawa Number Conjecture for semistable abelian varieties over finite unramified extensions of a function field of positive characteristic were obtained as a corollary of the result over p-adic Lie extensions (both last two results were the fruit of my collaboration with D. Vauclair).
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Research Products
(3 results)
