New developments of Iwasawa theory based on arithmetic topology

2017 Fiscal Year Final Research Report

• 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
• 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.

Free Research Field

代数的整数論