2010 Fiscal Year Final Research Report
New developments in number theory from the Kummer theory of algebraic tori
| Project/Area Number |
19540015
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
KIDA Masanari The University of Electro-Communications, 大学院・情報理工学研究科, 教授 (20272057)
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| Co-Investigator(Kenkyū-buntansha) |
OHNO Masahiro 電気通信大学, 大学院・情報理工学研究科, 准教授 (70277820)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 数論 |
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| Research Abstract |
In this research project, we are primarily concerned with a duality between the groups of rational points of algebraic tori and the Galois groups of maximal elementary abelian extensions over base fields without roots of unity. This is a natural generalization of the classical Kummer theory. We also compute generic polynomials for cyclic groups of small order in the case where the base field is a prime field. Several applications are also studied.
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