| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
The purpose of this research is to study the arithmetic geometry of Shimura varieties, and apply it to non-abelian class field theory. For this purpose, I organized several workshops on some topics including automorphic representations of classical groups, the cohomology of locally symmetric spaces, the Langlands correspondences over function fields, periods of automorphic representations, the trace formula, and promoted the study of Shimura varieties and related topics. Moreover, I investigated geometric and combinatorial aspects of Galois representations associated with plane curves, and obtained number theoretic results on the defining equations and symmetries of plane curves. I explicitly calculated the Galois action on 4-torsion points on the Fermat quartic. I investigated applications of geometric properties of orthogonal Shimura varieties to K3 surfaces.
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