| Project/Area Number |
26400018
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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 | Saga University |
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Principal Investigator |
ICHIKAWA Takashi 佐賀大学, 工学(系)研究科(研究院), 教授 (20201923)
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| Co-Investigator(Kenkyū-buntansha) |
中川 泰宏 佐賀大学, 工学(系)研究科(研究院), 教授 (90250662)
庄田 敏宏 佐賀大学, 教育学部, 准教授 (10432957)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 代数曲線 / モジュライ空間 / Chern-Simons不変量 / Arakelov理論 / Deligne-Riemann-Roch同型写像 / Schottky群 / Ruelleゼータ関数 / 数論幾何 / Riemann-Roch同型 / ゼータ関数 / アラケロフ幾何 / チャーン・サイモンズ不変量 / リウヴィル場 / 算術的リーマン・ロッホの定理 / アインシュタイン・ケーラー計量 / 極小曲面 / リーマン面 / ショットキー一意化 / リーマン・ロッホの定理 / 双曲３次元多様体 / チャーン・サイモンズ理論 |
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| Outline of Final Research Achievements |
By the arithmetic Schottky-Mumford uniformization theory, we proved the arithmeticity of Chern-Simons invariants. Using this result together with the Arakelov theory in arithmetic geometry and the theory of Zograf, Mcintyre-Takhatajan on the classical Liouville field theory, we gave an infinite product presentation of the Deligne-Riemann-Roch isomorphism which expresses the Chern-Simons line bundle. As its application, we express the special values of the Ruelle zeta functions of Schottky groups as the products of period integrals and discriminants. This result gives an analog of the Deligne conjecture on
such geometric zeta values.
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