Vol. 12, No. 10, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14, 1 issue

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Stark systems over Gorenstein local rings

Ryotaro Sakamoto

Vol. 12 (2018), No. 10, 2295–2326
Abstract

In this paper, we define a Stark system over a complete Gorenstein local ring with a finite residue field. Under some standard assumptions, we show that the module of Stark systems is free of rank 1 and that these systems control all the higher Fitting ideals of the Pontryagin dual of the dual Selmer group. This is a generalization of the theory, developed by B. Mazur and K. Rubin, on Stark (or Kolyvagin) systems over principal ideal local rings. Applying our result to a certain Selmer structure over the cyclotomic Iwasawa algebra, we propose a new method for controlling Selmer groups using Euler systems.

Keywords
Stark systems, Euler systems, Selmer groups, Iwasawa theory
Mathematical Subject Classification 2010
Primary: 11R23
Secondary: 11F80, 11S25
Milestones
Received: 19 April 2017
Revised: 26 February 2018
Accepted: 23 August 2018
Published: 1 February 2019
Authors
Ryotaro Sakamoto
Graduate School of Mathematical Sciences
The University of Tokyo
Tokyo
Japan