Algebra & Number Theory

Stark systems over Gorenstein local rings

Ryotaro Sakamoto

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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.

Article information

Source
Algebra Number Theory, Volume 12, Number 10 (2018), 2295-2326.

Dates
Received: 19 April 2017
Revised: 26 February 2018
Accepted: 23 August 2018
First available in Project Euclid: 14 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.ant/1550113224

Digital Object Identifier
doi:10.2140/ant.2018.12.2295

Mathematical Reviews number (MathSciNet)
MR3911132

Zentralblatt MATH identifier
07026819

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11F80: Galois representations 11S25: Galois cohomology [See also 12Gxx, 16H05]

Keywords
Stark systems Euler systems Selmer groups Iwasawa theory

Citation

Sakamoto, Ryotaro. Stark systems over Gorenstein local rings. Algebra Number Theory 12 (2018), no. 10, 2295--2326. doi:10.2140/ant.2018.12.2295. https://projecteuclid.org/euclid.ant/1550113224


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