p-adic Sato theory and arithmetic geometry
| Project/Area Number |
22654001
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Tohoku University |
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Principal Investigator |
YAMAZAKI Takao 東北大学, 大学院・理学研究科, 准教授 (00312794)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Shinichi 東北大学, 大学院・理学研究科, 准教授 (80362226)
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| Co-Investigator(Renkei-kenkyūsha) |
IKEDA Takeshi 岡山理科大学, 理学部, 准教授 (40309539)
YAMAZAKI Rei (YAMAZAKI INOUE Rei) 千葉大学, 理学部, 准教授 (30431901)
KONDO Satoshi 東京大学, 数物連携宇宙研究機構, 特任助教 (30372577)
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| Project Period (FY) |
2010 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,190,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2010: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | 数論幾何学 / 数理物理学 / タウ関数 / 佐藤理論 / ヤコビ多様体 / 佐藤グラスマン多様体 / テータ因子 / p-進佐藤理論 / 数論幾何 / 代数的完全可積分系 / 戸田格子 / マンフォード曲線 |
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| Research Abstract |
In order to clarify the integrable structure of non-linear PDEs such as KdV and KP equations, Mikio Sato introduced the tau function. Anderson introduced its p-adic analogue and applied it to arithmetic problem : a torsion point of"prime order" on the theta divisor of a Jacobian variety seldom exists. We extended this result to"prime power order". In the course of proving this result, we established many fundamental results on p-adic Sato theory, which are expected to be useful for other future research as well.
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Report
(3 results)
Research Products
(22 results)
