A study on K groups of the ring of integers of number fields

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400015
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Shimane University
• Principal Investigator: Aoki Miho 島根大学, 総合理工学研究科, 准教授 (10381451)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 代数的K群 / 岩澤加群 / イデアル類群 / 単数群 / Coates-Sinｎott予想 / CM体 / Fittingイデアル / 高次Stickelberger 元

Outline of Final Research Achievements

The results for the CM extension over the total real number field obtained in the previous research on the odd prime part of annihilator ideas of the K　groups of the ring of integers have been extended to the Fitting ideal under the technical assumption on the degree of the extension.
When the extension field is a CM field, the localization map of the cohomology group becomes complicated, compared to the case of the total real field,
but by decomposing the higher Stickelberger elements defined by the special values of the partial zeta function to the annihilators of the kernel and image of the localization map, we were able to obtain the results.

Free Research Field

数論