On potentially abelian geometric representations
type: Item
instance of: scholarly article
title: On potentially abelian geometric representations
zbMATH Open document ID: 1075.11043
author: Yuichiro Taguchi
published in: The Ramanujan Journal
publication date: 2004-05-27T00:00:00Z
review text: Let \(K\) be a number field, and fix a natural number \(d\) and a prime number \(p\). The author proves that there are only finitely many isomorphism classes of potentially abelian geometric Galois-representations \(G_K\rightarrow \text{GL}_d(\overline{{\mathbb Q}_p})\) with fixed Hodge-Tate-type and bounded inertial level. This proves the potentially abelian case of a more general conjecture of \textit{J.-M. Fontaine} and \textit{B. Mazur} in [Coates, John (ed.) et al., Elliptic curves, modular forms, \& Fermat's last theorem; Cambridge, MA: International Press. Ser. Number Theory. 1, 41--78 (1995; Zbl 0839.14011)].
reviewed by: Stefan Kühnlein
Mathematics Subject Classification ID: 11F80
Mathematics Subject Classification ID: 11G15
zbMATH DE Number: 2069234
zbMATH Keywords: geometric Galois representation
zbMATH Keywords: locally algebraic representation
zbMATH Keywords: finiteness conjecture of Fon\-taine-Mazur
MaRDI profile type: Publication
full work available at URL: b:rama.0000012429.09361.f5
OpenAlex ID: W2075736798
DOI: 10.1023/B:RAMA.0000012429.09361.F5
description: scientific article; zbMATH DE number 2069234