2018 Fiscal Year Final Research Report
| Project/Area Number |
15K04793
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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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 / Elliptic curve / Function fields |
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| Outline of Final Research Achievements |
We have established a foundation work generalizing the previous work of Kato -Trihan (this is now a submitted paper of more than 200 pages), proved the Iwasawa Main conjecture in two important cases : semistable abelian varieties over the arithmetic extension and constant ordinary abelian varieties over any Zp^d extensions ramifying at a finite set of places.
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| Free Research Field |
Mathematics
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| Academic Significance and Societal Importance of the Research Achievements |
The Iwasawa theory for abelian variety over the number fields was initiated in the 70s by Mazur. We give after Kato-Urban-Skinner the second case where the conjecture holds.
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