The number of monomial mod \(p\) Galois representations with bounded conductor
type: Item
instance of: scholarly article
title: The number of monomial mod \(p\) Galois representations with bounded conductor
zbMATH Open document ID: 1047.11050
author: Hyunsuk Moon
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2004-02-11T00:00:00Z
review text: This article gives an upper bound for the number of \(n\)-dimensional monomial representations of the absolute Galois group of \(\mathbb{Q}\) with values in a finite field of characteristic \(p\) and bounded conductor, and also a bound for the order of the image of such representations, in terms of \(n\), \(p\) and the conductor. Observe that in the non-monomial case (arbitrary \(n\)-dimensional mod \(p\) Galois representations with bounded conductor) the finiteness of the number of Galois representations is not known. Let us stress that to give an explicit bound is a much harder problem than to just prove finiteness (in the case of monomial representations, finiteness follows from the Hermite-Minkowski theorem and the finiteness of ray class groups). The proof uses bounds for discriminants of number fields, geometry of numbers and bounds for class numbers.
reviewed by: Luis Dieulefait
Mathematics Subject Classification ID: 11F80
zbMATH DE Number: 2040357
zbMATH Keywords: mod p Galois representations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113247447
OpenAlex ID: W2064668063
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DOI: 10.2748/TMJ/1113247447
description: scientific article; zbMATH DE number 2040357