| Project/Area Number |
20840022
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| Research Category |
Grant-in-Aid for Young Scientists (Start-up)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
MIZUSAWA Yasushi Nagoya Institute of Technology, 大学院・工学研究科, 准教授 (60453817)
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| Project Period (FY) |
2008 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2009: ¥988,000 (Direct Cost: ¥760,000、Indirect Cost: ¥228,000)
Fiscal Year 2008: ¥702,000 (Direct Cost: ¥540,000、Indirect Cost: ¥162,000)
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| Keywords | 代数的整数論 / 岩澤理論 / ガロア群 / 代数体 / Zp拡大 |
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| Research Abstract |
The Galois groups, which express the symmetry of the solutions of algebraic equations (roots of polynomials with integral coefficients), become the objects expressing a number of interesting properties (for example, uniqueness of prime factorization) of algebraic integers by considering the restricted ramifications. For a certain unsolved conjecture in Iwasawa theory, which concerns the prime factorization in higher dimensions, this research clarifies the non-commutative structures of certain Galois groups with restricted ramifications, and gave new affirmative examples of the conjecture by considering the non-commutative properties which are immanent in prime numbers.
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