On the image of \(l\)-adic Galois representations for abelian varieties of type I and II
type: Item
instance of: scholarly article
title: On the image of \(l\)-adic Galois representations for abelian varieties of type I and II
zbMATH Open document ID: 1186.11028
author: Grzegorz Banaszak
author: Wojciech Gajda
author: Piotr Krasoń
published in: Documenta Mathematica
publication date: 2007-06-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0407247
full work available at URL: https://eudml.org/doc/45100
full work available at URL: banaszak gajda krason.html
review text: Summary: In this paper we investigate the image of the \(l\)-adic representation attached to the Tate module of an abelian variety over a number field with endomorphism algebra of type I or II in the Albert classification. We compute the image explicitly and verify the classical conjectures of Mumford-Tate, Hodge, Lang and Tate for a large family of abelian varieties of type I and II. In addition, for this family, we prove an analogue of the open image theorem of Serre.
Mathematics Subject Classification ID: 11F80
Mathematics Subject Classification ID: 11G10
zbMATH DE Number: 5165894
zbMATH Keywords: abelian varieties
zbMATH Keywords: \(l\)-adic representations
MaRDI profile type: Publication
arXiv ID: math/0407247
description: scientific article