New development of non-commutative number theory

• Project/Area Number: 23654015
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Keio University
• Principal Investigator: KURIHARA Masato 慶應義塾大学, 理工学部, 教授 (40211221)
• Project Period (FY): 2011 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 数論 / イデアル類群 / 非可換拡大 / 整数論 / 国際研究者交流 / ドイツ

Research Abstract

We verified the non-commutative Brumer and Brumer-Stark conjectures by A. Nickel for various numerical examples for which one cannot apply the known theorems. We also studied the relationship between the non-commutative Brumer and Brumer-Stark conjectures

Research Products

• [Journal Article] Refined Iwasawa theory and Kolyvagin systems of Gauss sum type (2012)
  • Author(s): Masato Kurihara
  • Journal Title: Proceedings of the London Mathematical Society Volume: Vol.104 Pages: 728-769
  • Peer Reviewed
• [Journal Article] Ideal class groups of CM-fields with non-cyclic Galois action (2012)
  • Author(s): Masato Kurihara and Takashi Miura
  • Journal Title: Tokyo Journal of Mathematics Volume: Vol.35 Pages: 411-439
  • Peer Reviewed
• [Journal Article] On stronger versions of Brumer's conjecture (2012)
  • Author(s): Masato Kurihara
  • Journal Title: Tokyo Journal of Mathematics Volume: Vol.34-2 Pages: 407-428
  • Peer Reviewed
• [Presentation] Arithmetic of Kolyvagin systems of Gauss sum type for elliptic curves (2013)
  • Author(s): Masato Kurihara
  • Organizer: Number Theory Forum
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2013-03-25
• [Presentation] A refined Iwasawa theory and a refined Birch Swinnerton-Dyer conjecture (2013)
  • Author(s): Masato Kurihara
  • Organizer: Arithmetic and Algebraic Geometry 2013
  • Place of Presentation: 東京大学
  • Year and Date: 2013-01-30
• [Presentation] Brumer-Stark予想とGross予想について (2012)
  • Author(s): 栗原将人
  • Organizer: 第20回整数論サマースクール
  • Place of Presentation: 熊本県阿蘇郡高森町
  • Year and Date: 2012-09-05
• [Presentation] On the structure of ideal class groups and Selmer groups I, II, III (2012)
  • Author(s): Masato Kurihara
  • Organizer: L-functions and Arithmetic
  • Place of Presentation: Yonsei University, Korea
• [Presentation] On the Stickelberger elements and annihilation results for class groups I, II (2012)
  • Author(s): Masato Kurihara
  • Organizer: Iwasawa theory Workshop2012
  • Place of Presentation: 大阪大学
• [Presentation] On the structure of ideal class groups and Selmer groups I, II, III (2012)
  • Author(s): Masato Kurihara
  • Organizer: L-functions and Arithmetic
  • Place of Presentation: Yonsei University
  • Invited
• [Presentation] Euler systems of Gauss sum type and the structure of Selmer modules (2011)
  • Author(s): Masato Kurihara
  • Organizer: The 3rd Pan Asian Number Theory Conference
  • Place of Presentation: Chinese Academy of Sciences, Beijing、China
  • Year and Date: 2011-08-25
• [Presentation] Euler systems of Gauss sum type and the structure of Selmer modules (2011)
  • Author(s): Masato Kurihara
  • Organizer: The 3rd Pan Asian Number Theory Conference(招待講演)
  • Place of Presentation: Chinese Academy of Sciences, 北京、中国