Refinement of Iwasawa theory and its applications

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800011
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Ehime University
• Principal Investigator: Ohshita Tatsuya 愛媛大学, 理工学研究科(理学系), 助教 (70712420)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 岩澤理論 / Euler系 / Galois変形 / 高次Fittingイデアル

Outline of Final Research Achievements

Roughly speaking, Iwasawa theory is a research area of number theory which studies mysterious relationships between algebraic objects, like ideal class groups, and analytic objects, like special values of zeta functions, lying in the p-adic world (for a fixed prime number p). In Iwasawa theory, systems of Galois cohomology classes called "Euler systems" play roles as bridges between algebraic objects and analytic ones.
In our work, in order to obtain refinements of Iwasawa theory, we have tried to construct a theory which describes finer information on algebraic objects by using Euler systems. By our investigation, in particular, by using Kolyvagin derivatives of rank one Euler systems of Rubin type (satisfying certain good conditions) for a given Galois deformation, we have constructed certain ideals of the deformation ring which determine the pseudo-isomorphism class of the dual fine Selmer group of the Galois deformation.

Free Research Field

整数論