2013 Fiscal Year Final Research Report
A study on constructive inverse Galois problem
| Project/Area Number |
22740028
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Rikkyo University
Niigata University |
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Principal Investigator |
HOSHI Akinari 新潟大学, 自然科学系, 准教授 (50434262)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | ガロア逆問題 / ネーター問題 / 有理性問題 / 双有理分類 / 不分岐ブラウアー群 / 安定有理性 / レトラクト有理性 / Thue方程式 |
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| Research Abstract |
Galois theory, forms the foundation of modern algebra, founded by Evariste Galois has continued to support the development of state-of-the-art mathematics. In Galois theory, the problem "whether every finite group appears as the Galois group of some field extension or not" is called inverse Galois problem, and is related to the structure of the absolute Galois group of rationals which is an interesting subject in number theory.
In this research, we gave answers to some problems, e.g. Noether's problem, the field isomorphism problem of generic polynomials, which are related to the inverse Galois problem. By applying this, we also solved some Thue equations.
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