2016 Fiscal Year Final Research Report
Study on regulator maps using the theory of Arakelov geometry
| Project/Area Number |
25400017
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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 | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | アラケロフ幾何学 |
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| Outline of Final Research Achievements |
We have made researches in order to formulate and prove higher arithmetic Riemann-Roch theorem. To be more precise, we have tried to construct the theory of higher analytic torsion forms associated with Hermitian vector bundles on an iterated double. We have found a sufficient condition under which the proof of the higher arithmetic Riemann-Roch theorem goes well.
We have made researches on a special class of partitions of natural numbers called t-core. We have found quadratic forms which are closely related to t-core partitions. We have given a purely combinatorial method to prove congruence conditions on numbers of t-core partitions. It relies on the theory of quadratic forms and geometry on finite fields.
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| Free Research Field |
数論幾何学
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