On a lemma of Ribet.
type: Item
instance of: scholarly article
title: On a lemma of Ribet.
zbMATH Open document ID: 1048.20032
author: Joël Bellaïche
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2004-09-07T00:00:00Z
review text: Let \(R\) be a discrete complete valuation ring, \(K\) its fraction field, \(k\) the residue field, and \(V\) an \(n\)-dimensional \(K\)-vector space. Consider an irreducible representation \(\rho\colon G\to\text{GL}(V)\) of a group \(G\) which stabilizes a lattice \(\Lambda\subset V\); this defines a representation \(\overline\rho\colon G\to\text{GL}(n,k)\). The main result of this paper consists in finding extensions between factors of \(\overline\rho\). The case \(n=2\) is an important lemma of \textit{K. A. Ribet} [Invent. Math. 34, 151-162 (1976; Zbl 0338.12003)].
Mathematics Subject Classification ID: 20G25
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 2099240
zbMATH Keywords: local fields
zbMATH Keywords: irreducible representations
zbMATH Keywords: extensions of representations
zbMATH Keywords: Ribet lemma
zbMATH Keywords: Bruhat-Tits construction
reviewed by: Marcel Morales
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2099240