Stratifications of the moduli space of abelian varieties and that of curves
| Project/Area Number |
17K05196
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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 | Yokohama National University |
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Principal Investigator |
Shushi Harashita 横浜国立大学, 大学院環境情報研究院, 准教授 (70396852)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 代数幾何学 / アーベル多様体 / 代数曲線 / モジュライ空間 / 超特異 / 曲線 / 超特異曲線 / 超特別曲線 / Newton polygon / 最大曲線 / p-可除群 / 階層構造 |
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| Outline of Final Research Achievements |
Abelian varieties and algebraic curves treated in this research play central roles in algebraic geometry of mathematics and have many applications in other areas. Socially, there are objects (supersingular curves) that will be used in next-generation information technology such as post-quantum cryptography, and we are intensely studying those objects. As research results, we determine specializations of p-divisible groups (which are attached to abelian varieties and algebraic curves) and enumerate superspecial curves (of various types) of low genera and in small characteristics (using PC computations), and show the existence of a superspecial curve of genus 4 in arbitrary characteristic (theoretical result) and so on.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では、アーベル多様体や代数曲線のモジュライ空間に入る階層構造や葉層構造を系統的に研究している。理論的研究と共に、応用面でも利用される超特異アーベル多様体や超特異代数曲線、またそれらのなす空間についても深く調査している。特に、超特異代数曲線やそれらの間の同種写像は、耐量子計算機暗号等にも用いられ、本研究が社会的に意義のある成果を生み出す可能性がある。
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Report
(5 results)
Research Products
(20 results)
