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2016 Fiscal Year Final Research Report

Study on regulator maps using the theory of Arakelov geometry

Research Project

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Project/Area Number 25400017
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionKyushu University

Principal Investigator

Takeda Yuichiro  九州大学, 数理学研究院, 准教授 (30264584)

Project Period (FY) 2013-04-01 – 2017-03-31
Keywordsアラケロフ幾何学
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.

Free Research Field

数論幾何学

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Published: 2018-03-22  

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