Research on the structure of Iwasawa modules for p-adic representations

• Project/Area Number: 21540018
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Hiroshima University
• Principal Investigator: TAKAHASHI Hiroki 広島大学, 理学研究科, 准教授 (90291476)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 岩澤加群 / イデアル類群 / Greenberg 予想 / 円単数 / ガウス和 / 岩澤不変量 / Greenberg予想 / Kummer-Vandiver予想 / p進L関数 / 一般Greenberg予想 / 岩澤多項式 / Eisensteinイデアル

Research Abstract

In this research, we investigated concrete structure of Iwasawa modules for p-adic representations by systematic use of specialelements. We especially noticed large Iwasawa lambda or nu invariants. We computed these invariants of the rational number field and 122 quadratic fields with the discriminant D

Research Products

• [Journal Article] On the Iwasawa lambda invariant of an imaginary abelian field of conductor 3p^n+1 (2013)
  • Author(s): H. Ichimura, S. Nakajima, H. Sumida-Takahashi
  • Journal Title: Journal of Number Theory Volume: 133 Pages: 787-801
  • Peer Reviewed
• [Journal Article] On the Iwasawa lambda invariant of an imaginary abelian field of conductor 3p^{n+1} (2013)
  • Author(s): Humio Ichimura, Shoichi Nakajima, Hiroki Sumida-Takahashi
  • Journal Title: Journal of Number Theory Volume: 133 Issue: 2 Pages: 787-801
  • DOI: 10.1016/j.jnt.2012.08.022
  • Peer Reviewed
• [Journal Article] On Hilbert-Speiser type imaginary quadratic fields (2009)
  • Author(s): H. Ichimura, H. Sumida-Takahashi
  • Journal Title: Acta Arithmetica Volume: 136 Pages: 385-38
  • Peer Reviewed
• [Journal Article] On Hilbert-Speiser type imaginary quadratic fields (2009)
  • Author(s): Humio Ichimura, Hiroki Sumida-Takahashi
  • Journal Title: Acta Arithmetica 136 Pages: 385-389
  • Peer Reviewed
• [Presentation] The Iwasawaλ_l-invariants in cyclotomic Z_p-extensions (2013)
  • Author(s): 高橋浩樹
  • Organizer: 早稲田整数論研究集会
  • Place of Presentation: 東京
  • Year and Date: 2013-03-16
• [Presentation] 円分体の岩澤不変量の観察 (2012)
  • Author(s): 高橋浩樹
  • Organizer: 九州代数的整数論2012
  • Place of Presentation: 福岡
  • Year and Date: 2012-03-23
• [Presentation] 円分体の岩澤不変量の観察 (2012)
  • Author(s): 高橋浩樹
  • Organizer: 九州代数的整数論2012
  • Place of Presentation: 福岡市(招待講演)
  • Year and Date: 2012-02-23
• [Presentation] The Iwasawa λ_l invariants in cyclotomic Z_p-extensions
  • Author(s): 高橋浩樹
  • Organizer: 2013早稲田整数論研究集会
  • Place of Presentation: 早稲田大学
  • Invited
• [Remarks]
  • URL: http://www.mis.hiroshima-u.ac.jp/hiroki/major/galois1.html
• [Remarks]
  • URL: http://www.mis.hiroshima-u.ac.jp/~hiroki/major/galois1.html
• [Remarks]
  • URL: http://www.mis.hiroshima-u.ac.jp/~hiroki/major/galois.html