Explicit surjectivity of Galois representations for abelian surfaces and \(\operatorname{GL}_{2}\)-varieties
type: Item
instance of: scholarly article
title: Explicit surjectivity of Galois representations for abelian surfaces and \(\operatorname{GL}_{2}\)-varieties
zbMATH Open document ID: 1343.11058
author: Davide Lombardo
published in: Journal of Algebra
publication date: 2016-06-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1411.1703
reviewed by: Remke Kloosterman
Mathematics Subject Classification ID: 11G10
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 11F80
zbMATH DE Number: 6597440
zbMATH Keywords: abelian varieties
zbMATH Keywords: Galois representations
zbMATH Keywords: Tate module
MaRDI profile type: Publication
OpenAlex ID: W2346767626
arXiv ID: 1411.1703
cites work: On the maximal subgroups of the finite classical groups
cites work: On the image of \(l\)-adic Galois representations for abelian varieties of type I and II
cites work: Q4830002
cites work: The Subgroups of PSL(3, q) for odd q
cites work: The maximal subgroups of the low-dimensional finite classical groups.
cites work: ℓ-Adic and λ-Adic Representations Associated to Abelian Varieties Defined Over Number Fields
cites work: Explicit Determination of the Images of the Galois Representations Attached to Abelian Surfaces with End(A) = Z
cites work: The arithmetic of QM-abelian surfaces through their Galois representations
cites work: Polarization and isogenies
cites work: Period theorem and minimal degrees of isogenies
cites work: On uniform large Galois images for modular abelian varieties
cites work: Modeles de neron et monodromie
cites work: An open-image theorem for a general class of abelian varieties
cites work: Galois theory of iterated endomorphisms
cites work: The effective surjectivity of \(\mod l\) Galois representations of 1- and 2-dimensional abelian varieties with trivial endomorphism ring
cites work: Serre's modularity conjecture. I
cites work: Serre's modularity conjecture. II
cites work: Determinants of subquotients of Galois representations associated with abelian varieties
cites work: Bounds for Serre's open image theorem for elliptic curves over number fields
cites work: Galois Properties of Division Fields of Elliptic Curves
cites work: Isogeny estimates for abelian varieties, and finiteness theorems
cites work: Periods and minimal abelian subvarieties
cites work: Varieties Defined by Quadratic Equations
cites work: Q4078163
cites work: ℓ-adic algebraic monodromy groups, cocharacters, and the MumfordTate conjecture
cites work: Schémas en groupes de type $(p,\ldots,p)$
cites work: Q4414310
cites work: Galois Action on Division Points of Abelian Varieties with Real Multiplications
cites work: Q4214907
cites work: Galois properties of points of finite order of elliptic curves
cites work: Fields of definition for homomorphisms of abelian varieties
cites work: Q5200681
DOI: 10.1016/J.JALGEBRA.2016.04.011
review text: Let \(A\) be an absolutely simple abelian variety defined over a number field \(K\), without potential complex multiplication. Suppose that \(\dim A=2\) or that \(A\) is of \(\mathrm{GL}_2\)-type, i.e., \(\mathrm{End}_{\overline{K}}(A)\otimes \mathbb{Q}\) is a totally real number, of degree \(\dim A\) over \(\mathbb{Q}\).NEWLINENEWLINEThe author gives an \textit{explicit} bound \(\ell_0\), depending only on \(A\) and \(K\), such that for each each prime \(\ell>\ell_0\) the image of \(\mathrm{Gal}(\overline{K}/K)\) in \(\mathrm{Aut}(T_\ell(A))\) is as large as possible.
description: scientific article; zbMATH DE number 6597440