| Project/Area Number |
26400024
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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 | Chuo University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | Kummer理論 / group scheme / algebraic torus / torsor / Hopf代数 / Hopf-Galois理論 / Artin-Schreier理論 / 正規底 / Hopf-Galois拡大 |
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| Outline of Final Research Achievements |
It is a main purpose of our research to study the inverse Galois problem, which is one of the most important in the Galois theory.
We discuss the inverse Galois problem with normal basis, concerning Kummer theories for algebraic tori not only over a field but also over a ring, in the framework of group schemes. The unit group scheme of a group algebra plays an important role in this article, as was pointed out by Serre <Groupes algebriques et corps de classes>. We also formulate the notion of cleft extensions in the Hopf-Galois theory in the framework of algebraic geometry. The unit group scheme of the algebra of a finite flat group scheme plays a key role.
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