Study on a refinement of Iwasawa theory with a focus on the Brumer-Stark conjecture

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800024
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tsuruoka National College of Technology
• Principal Investigator: Miura Takashi 鶴岡工業高等専門学校, その他部局等, 助教 (60631934)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 整数論 / 岩澤理論 / イデアル類群

Outline of Final Research Achievements

We make a study on describing the Fitting ideal of the ideal class group of a number field by using special values of L-functions, which we may regard as a certain type of refinement of Iwasawa theory. We have almost determined under certain conditions the Fitting ideal of the ideal class group of a CM-field which is abelian over a totally real number field whose Galois group is not similar to that of the cyclotomic fileds. Namely we studied the case that the Galois group is not isomorphic to the direct product of the inertia groups of ramifying primes. Applying such a method as used in the research on the ideal class gropus to investigating the ray class groups, we also make a study on a certain type of refinement of the Brumer-Stark conjecture and obtain partial results.

Free Research Field

代数学