Torseurs pour les motifs et pour les représentations p-adiques potentiellement de type CM. (Torsors for motives and for p-adic representations potentially of CM type)
type: Item
instance of: scholarly article
title: Torseurs pour les motifs et pour les représentations p-adiques potentiellement de type CM. (Torsors for motives and for p-adic representations potentially of CM type)
zbMATH Open document ID: 0711.14028
DOI: 10.1007/BF01444517
author: Jean-Pierre Wintenberger
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164719
review text: The Betti cohomology fibre functor \(H_ B\) and the De Rham cohomology fibre functor \(H_{DR}\) on the category of abelian varieties over \({\mathbb{Q}}\) of CM-type are realizations of the motives over \({\mathbb{Q}}\) with absolute Hodge cycles. Let G be the tensor automorphism group of \(H_ B\) (the Taniyama group) and P the G-torsor of tensor isomorphisms \(H_{DR}\to H_ B\). One determines the cohomology class of P in \(H^ 1({\mathbb{Q}},G)\). A similar cohomology class is determined in a p-adic context, where now G is the group of tensor automorphisms of the fibre functor that associates to a p-adic representation of the Galois group of the algebraic p-adic numbers its representation space and P is the G- torsor of the tensor isomorphisms of P to a fibre functor involving Hodge-Tate modules. The connection of the two situations is indicated.
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14A20
Mathematics Subject Classification ID: 14K22
Mathematics Subject Classification ID: 14F40
zbMATH DE Number: 4168835
zbMATH Keywords: abelian varieties of CM-type
zbMATH Keywords: motives
zbMATH Keywords: absolute Hodge cycles
zbMATH Keywords: torsor
reviewed by: J. H. de Boer
MaRDI profile type: Publication
cites work: Q3322215
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OpenAlex ID: W1978052981
description: scientific article; zbMATH DE number 4168835