2013 Fiscal Year Final Research Report
Around Kummer theories, from the view point of group schemes
| Project/Area Number |
23540027
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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) |
2011 – 2013
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| Keywords | Kummer理論 / Artin-Schreier理論 / group scheme / torsor / Hopf代数 / Hopf-Galois理論 |
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| Research Abstract |
It is a main purpose of our research to formulate and develop the theories analogous to the Kummer and Artin-Schreier theories, which are important items of the Galois theory and the starting points of the theory of etale cohomology. Needless to say, the Galois theory is a basis of the modern algebra. And the theory of etale cohomology provides us with a powerful tool in arithmetic geometry, which has developed vastly during the past half a century.
In particular we obtain several results for finite flat group schemes, concerning to relations between normal bases of a cleft Hopf-Galois extension and the unit group scheme of a finite flat group scheme. This is a natural generalization of Serre's arugument on relations between normal bases of a Galois extension of fields and the unit group of the group algebra of a finite groups.
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