New progress of number theoy by developing Kummer theory of algebraic groups

2009 Fiscal Year Self-evaluation Report

• 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, 電気通信学部, 教授 (20272057)
• Project Period (FY): 2007 – 2010
• Keywords: 代数的整数論 / ガロア理論 / クンマー理論

Research Abstract

乗法群のべき乗写像の代わりに、可換代数群とその間の同種写像をとって得られる新しいタイプのクンマー理論についての研究である。基礎理論の確立とその数論的な問題への応用を目標にしている。

Research Products

• [Journal Article] Descent Kummer theory via Weil restriction of multiplicative groups (2010)
  • Author(s): Kida, Masanari
  • Journal Title: J.Number Theory 130 Pages: 639-659
  • Peer Reviewed
• [Journal Article] Kazuhiro : Quintic polynomials of Hashimoto-Tsunogai, Brumer, and Kummer (2009)
  • Author(s): Kida, Masanari, Renault, Guenael, Yokoyama
  • Journal Title: Int. J. Number Theory 5 Pages: 555-571
  • Peer Reviewed
• [Presentation] Constructing metacyclic extensions. First PRIMA Congress. (2009)
  • Author(s): Masanari Kida
  • Organizer: The University of New South Wales
  • Place of Presentation: Sydney, Australia
  • Year and Date: 2009-07-10
• [Presentation] On metacyclic extensions (2008)
  • Author(s): 木田雅成
  • Organizer: 研究集会「ガロア理論とその周辺徳島2008」
  • Place of Presentation: 徳島大学工業会館
  • Year and Date: 2008-09-09
• [Presentation] Classification of Brumer's quintic dihedral polynomials (2008)
  • Author(s): Masanari Kida
  • Organizer: Foundation of Computational Mathematics (FoCM08) Computational Number Theory Workshop
  • Place of Presentation: City University of Hong Kong
  • Year and Date: 2008-06-25
• [Presentation] D_5拡大のクンマー理論 (2008)
  • Author(s): 木田雅成
  • Organizer: 第13回早稲田大学整数論研究集会
  • Place of Presentation: 早稲田大学理工学部
  • Year and Date: 2008-03-11
• [Presentation] A classification of isomorphic classes of Brumer's quintic polynomials using elliptic curves (2007)
  • Author(s): 木田雅成, 陸名雄一
  • Organizer: 研究集会「ガロア理論とその周辺」
  • Place of Presentation: 山形大学理学部
  • Year and Date: 2007-11-03
• [Presentation] Brumer の多項式の分解体について (2007)
  • Author(s): 木田雅成
  • Organizer: 日本数学会2007年度秋季総合分科会
  • Place of Presentation: 東北大学理学部
  • Year and Date: 2007-09-23
• [Remarks]
  • URL: http://mathweb.e-one.uec.ac.jp/~kida