| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We obtained a sufficient condition of non-existence of rational points over number fields on Shimura curves defined over the field of rational numbers. As an application, we obtained an explicit infinite family of counterexamples to the Hasse principle. Furthermore, we proved that such coounterexamples are accounted for by the Manin obstruction.
We also obtained a sufficient condition of non-existence of higher dimensional abelian varieties in explicit terms of algebraic number theory. Furthermore, we obtained a necessary and sufficient condition for abelian varieties over finite fields of having QM.
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