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2018 Stark systems over Gorenstein local rings
Ryotaro Sakamoto
Algebra Number Theory 12(10): 2295-2326 (2018). DOI: 10.2140/ant.2018.12.2295

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.

Citation

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Ryotaro Sakamoto. "Stark systems over Gorenstein local rings." Algebra Number Theory 12 (10) 2295 - 2326, 2018. https://doi.org/10.2140/ant.2018.12.2295

Information

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

zbMATH: 07026819
MathSciNet: MR3911132
Digital Object Identifier: 10.2140/ant.2018.12.2295

Subjects:
Primary: 11R23
Secondary: 11F80, 11S25

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.12 • No. 10 • 2018
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