Lifting according to an isogeny of \(\ell\)-adic Galois representations associated to motives
type: Item
instance of: scholarly article
title: Lifting according to an isogeny of \(\ell\)-adic Galois representations associated to motives
zbMATH Open document ID: 0870.11031
DOI: 10.1007/BF01241127
author: Jean-Pierre Wintenberger
published in: Inventiones Mathematicae
publication date: 1995-08-29T00:00:00Z
full work available at URL: https://eudml.org/doc/144274
review text: Let \(E/\mathbb{Q}\) be a number field and write \(G_E= \text{Gal} (\overline{\mathbb{Q}}/E)\). Let \(H/\mathbb{Q}\) be an algebraic group and let \((\rho_\ell)\) be a system of \(\ell\)-adic Galois representations of \(G_E\) with values in \(H\). Suppose that \((\rho_\ell)\) is associated to a motive defined over \(E\). Let \(H'\to H\) be a central isogeny such that the complex Hodge structure lifts to \(H'\). The main result of the paper then states (under some mild hypothesis) that after restriction to a finite extension \(E'/E\) the system \((\rho_\ell)\) lifts to \(H'\).
reviewed by: Winfried Kohnen
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F85
Mathematics Subject Classification ID: 11G09
Mathematics Subject Classification ID: 14A20
Mathematics Subject Classification ID: 14C30
zbMATH DE Number: 784000
zbMATH Keywords: \(\ell\)-adic Galois representations associated to a motive
zbMATH Keywords: liftings
zbMATH Keywords: central isogeny
MaRDI profile type: Publication
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OpenAlex ID: W2914242903
description: scientific article; zbMATH DE number 784000