Analysis of the structures of Iwasawa modules by arithmetic special elements

2017 Fiscal Year Final Research Report

• Project/Area Number: 25400013
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokushima
• Principal Investigator: TAKAHASHI HIROKI 徳島大学, 大学院社会産業理工学研究部(理工学域), 教授 (90291476)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: Greenberg予想 / 一般Greenberg予想 / 岩澤加群 / 円単数 / 岩澤不変量

Outline of Final Research Achievements

The purpose of this research was to investigate concrete structures of Iwasawa modules associated to various p-adic Galois representations by using special elements, and to clarify detailed reasons of Greenberg's conjecture for totally real number fields and Greenberg's generalized conjecture for general algebraic number fields. Concerning the former conjecture, we computed structures of Iwasawa modules for cyclotomic Z_p-extensions of composite fields of p-cyclotomic fields and quadratic fields with the discriminant D<10 (resp.D<200) in the range 6,000,000<p<13,000,000 (resp. 300,000<p<600,000), and checked that the actual numbers are close to the expected numbers. Concerning the latter conjecture, we computed paring of p-unit groups of 4p-cyclotomic fields for Milnor K_2-groups in the range p<32768, and checked that the actual numbers of nontrivial zeros are close to the expected numbers.

Free Research Field

整数論