New developments of Iwasawa theory based on arithmetic topology

• Project/Area Number: 26800010
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Nagoya Institute of Technology
• Principal Investigator: Mizusawa Yasushi 名古屋工業大学, 工学(系)研究科(研究院), 准教授 (60453817)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 岩澤理論 / 数論的トポロジー / 馴分岐 / ガロア群

Outline of Final Research Achievements

The main purpose of this research is a contribution to Iwasawa theory from a view point of arithmetic topology. The main objects are the structural invariants of Galois groups of number fields with restricted ramification. This research provided various description of the nonabelian structure of pro-p Galois groups. In particular when the ramification at p is restricted cyclotomically, some invariants in Iwasawa theory were computed from the nonabelian structure of the Galois groups which are described as analogues of link groups.

Research Products

• [Journal Article] Tame pro-2 Galois groups and the basic Z_2-extension (2018)
  • Author(s): Yasushi Mizusawa
  • Journal Title: Transactions of the American Mathematical Society Volume: 370 Issue: 4 Pages: 2423-2461
  • DOI: 10.1090/tran/7023
  • Peer Reviewed
• [Journal Article] On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field (2018)
  • Author(s): Amano Fumiya、Mizusawa Yasushi、Morishita Masanori
  • Journal Title: Research in Number Theory Volume: 4 Issue: 1 Pages: 1-29
  • DOI: 10.1007/s40993-018-0100-7
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On certain 2-extensions of $\mathbb{Q}$ unramified at 2 and $\infty$ (2016)
  • Author(s): Yasushi Mizusawa
  • Journal Title: Osaka Journal of Mathematics Volume: 53 Pages: 1063-1088
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] On 2-adic L-functions and the pro-2 Fox derivative (2018)
  • Author(s): 水澤靖
  • Organizer: 第11回ゼータ若手研究集会
  • Invited
• [Presentation] 代数体の副p絡み目群について (2017)
  • Author(s): 水澤 靖
  • Organizer: 2017早稲田整数論研究集会
  • Place of Presentation: 早稲田大学西早稲田キャンパス（東京都新宿区）
  • Year and Date: 2017-03-22
• [Presentation] On pro-p link groups of number fields (2017)
  • Author(s): Yasushi Mizusawa
  • Organizer: Low dimensional topology and number theory IX
  • Place of Presentation: AiRIMaQ Seminar Room, Innovation Plaza（福岡市百道浜）
  • Year and Date: 2017-03-17
• [Presentation] Pro-p link groups in Iwasawa theory (2017)
  • Author(s): Yasushi Mizusawa
  • Organizer: Iwasawa 2017
  • Int'l Joint Research
• [Presentation] 代数体の副p絡み目群について (2016)
  • Author(s): 水澤 靖
  • Organizer: 北陸数論研究集会2016
  • Place of Presentation: 金沢大学サテライトプラザ（石川県金沢市）
  • Year and Date: 2016-12-26
• [Presentation] 代数体の副p絡み目群について (2016)
  • Author(s): 水澤 靖
  • Organizer: 新潟代数セミナー
  • Place of Presentation: 新潟大学（新潟市）
  • Year and Date: 2016-12-23
• [Presentation] On certain 2-extensions of $\mathbb{Q}$ unramified at 2 and $\infty$ (2016)
  • Author(s): Yasushi Mizusawa
  • Organizer: Christian Maire氏を囲んでの小研究集会
  • Place of Presentation: 早稲田大学西早稲田キャンパス（東京都新宿区）
  • Year and Date: 2016-05-16
• [Presentation] Tame pro-p Galois groups over cyclotomic Zp-extensions (2016)
  • Author(s): Yasushi Mizusawa
  • Organizer: Low dimensional topology and number theory VIII
  • Place of Presentation: IMAQ Seminar Room, Innovation Plaza, Fukuoka
  • Year and Date: 2016-03-22
  • Int'l Joint Research
• [Presentation] ある総実馴分岐2-拡大のガロア群について (2015)
  • Author(s): 水澤 靖
  • Organizer: 日本数学会2015年度秋季総合分科会代数学分科会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-16
• [Presentation] 基本Z2拡大上の馴分岐pro-2ガロア群について (2015)
  • Author(s): 水澤 靖
  • Organizer: 日本数学会2015年度秋季総合分科会代数学分科会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-16
• [Presentation] ある総実馴分岐2-拡大のガロア群について (2014)
  • Author(s): 水澤 靖
  • Organizer: 愛知数論セミナー
  • Place of Presentation: 名古屋工業大学
  • Year and Date: 2014-10-11