| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
The problem on rational points is a basic problem in number theory; it is related to solving equations defined by polynomials. On the other hand, the problem on rational points on moduli spaces is an important subject in arithmetic geometry; it is also related to classifying geometric objects corresponding to rational points.
In this research, we have determined possible characters appearing in the Galois representations associated to abelian varieties. Also, by using this result, we have obtained criteria of non-existence of rational points on a Shimura curve, which is a certain moduli space of abelian varieties. Furthermore, we have several numerical examples, which make the results visible.
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