Global quadratic units and Hecke algebras
type: Item
instance of: scholarly article
title: Global quadratic units and Hecke algebras
zbMATH Open document ID: 0923.11084
author: Haruzo Hida
published in: Documenta Mathematica
publication date: 1998-11-22T00:00:00Z
full work available at URL: https://eudml.org/doc/226045
full work available at URL: 10.html
review text: Summary: Let \(\{\rho_{\mathfrak p}\}_{\mathfrak p}\) be a compatible system of two dimensional \({\mathfrak p}\)--adic Galois representations attached to a cusp form of nebentype \(({D\over })\) (\(D>0\)). The author gives an exact criterion, in terms of the fundamental unit \(\varepsilon\) of \({\mathbb Q}(\sqrt{D})\), determining primes \({\mathfrak p}\) for which the image of \(\rho_{\mathfrak p}\mod{\mathfrak p}\) is dihedral. Then he states a conjecture which gives an explicit description of the universal \(p\)-ordinary deformation ring of such mod \({\mathfrak p}\) dihedral representations.
Mathematics Subject Classification ID: 11F80
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 1225038
zbMATH Keywords: global quadratic units
zbMATH Keywords: Hecke algebra
zbMATH Keywords: \({\mathfrak p}\)-adic Galois representations
zbMATH Keywords: fundamental unit
zbMATH Keywords: universal \(p\)-ordinary deformation ring
zbMATH Keywords: dihedral representations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1225038