New developments in number theory from the Kummer theory of algebraic tori
Project/Area Number |
19540015
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | The University of Electro-Communications |
Principal Investigator |
KIDA Masanari The University of Electro-Communications, 大学院・情報理工学研究科, 教授 (20272057)
|
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)
|
Project Period (FY) |
2007 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 数論 / クンマー理論 / 逆ガロア問題 / 代数的トーラス / イデアル類群 / 代数的整数論 / ガロア理論 / 代数群 / クンマー拡大 / 生成的多項式 / 巡回拡大 / Brumerの多項式 |
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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Report
(6 results)
Research Products
(37 results)