| 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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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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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 / Bogomolov multiplier / 同型問題 / 単純巡回多項式 / 生成的多項式 / 共通部分体問題 / 振れ対称群作用 |
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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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