The algebraic functional equation of Selmer groups for CM fields
type: Item
instance of: scholarly article
title: The algebraic functional equation of Selmer groups for CM fields
zbMATH Open document ID: 1209.11094
author: Ming-Lun Hsieh
published in: Journal of Number Theory
publication date: 2010-07-22T00:00:00Z
review text: The author proves the algebraic functional equation for the Selmer groups of CM fields. This functional equation is predicted by a corresponding analytic functional equation and the Iwasawa main conjecture. The author uses the specialisation technique developed by Ochiai.
reviewed by: R. Sujatha
Mathematics Subject Classification ID: 11R23
zbMATH DE Number: 5759062
zbMATH Keywords: Iwasawa theory
zbMATH Keywords: functional equation
zbMATH Keywords: Main conjecture
MaRDI profile type: Publication
full work available at URL: j.jnt.2010.02.003
OpenAlex ID: W2002747329
cites work: Q5515450
cites work: Onp-adicL-functions and cyclotomic fields. II
cites work: Q3972988
cites work: Q4297081
cites work: On the Iwasawa invariants of elliptic curves
cites work: Q4490714
cites work: Q3972777
cites work: Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules
cites work: On the anticyclotomic main conjecture for CM fields
cites work: \(p\)-adic \(L\)-functions for CM fields
cites work: Q3754095
cites work: Euler system for Galois deformations.
cites work: The algebraic \(p\)-adic \(L\)-function and isogeny between families of Galois representations
cites work: The ``main conjectures'' of Iwasawa theory for imaginary quadratic fields
DOI: 10.1016/J.JNT.2010.02.003
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description: scientific article; zbMATH DE number 5759062