2009 Fiscal Year Final Research Report

Iwasawa theoretical studies of Galois groups over algebraic number fields with restricted ramifications

Research Project

Project/Area Number	20840022
Research Category	Grant-in-Aid for Young Scientists (Start-up)
Allocation Type	Single-year Grants
Research Field	Algebra
Research Institution	Nagoya Institute of Technology
Principal Investigator	MIZUSAWA Yasushi Nagoya Institute of Technology, 大学院・工学研究科, 准教授 (60453817)
Project Period (FY)	2008 – 2009
Keywords	代数的整数論 / 岩澤理論 / ガロア群 / 代数体
Research Abstract	The Galois groups, which express the symmetry of the solutions of algebraic equations (roots of polynomials with integral coefficients), become the objects expressing a number of interesting properties (for example, uniqueness of prime factorization) of algebraic integers by considering the restricted ramifications. For a certain unsolved conjecture in Iwasawa theory, which concerns the prime factorization in higher dimensions, this research clarifies the non-commutative structures of certain Galois groups with restricted ramifications, and gave new affirmative examples of the conjecture by considering the non-commutative properties which are immanent in prime numbers.