On fields of definition of torsion points of elliptic curves with complex multiplication

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 09 Nov 2010Embargo end date: 01 Jan 2009 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 139, pages 1,961-1,969 (issn: 0002-9939, eissn: 1088-6826,

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Authors: Dieulefait, Luis Victor; Gonzalez Jimenez, Enrique; Jiménez Urroz, Jorge;

doi: 10.1090/s0002-9939-2010-10621-4 , 10.48550/arxiv.0909.1661

arXiv: 0909.1661

handle: 2117/12251 , 2445/96600 , 10486/711200

On fields of definition of torsion points of elliptic curves with complex multiplication

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Abstract

For any elliptic curve E defined over the rationals with complex multiplication and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of definition of torsion points of these curves, in particular we classify all cases where there are torsion points over Galois number fields not containing the field of definition of the CM.

To appear in Proceeding of the American Mathematical Society

Related Organizations

Spanish National Research Council
Spain
University of Barcelona
Spain
Universitat Polite`cnica de Catalunya
Spain
Autonomous University of Madrid
Spain
Universitat Politècnica de Catalunya
Spain

Keywords

Torsion, Grups discontinus, Matemáticas, Galois theory, Classificació AMS::11 Number theory::11F Discontinuous groups and automorphic forms, Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry), Torsió, :11 Number theory::11F Discontinuous groups and automorphic forms [Classificació AMS], FOS: Mathematics, Geometria algebraica aritmètica, Elliptic curves, Number Theory (math.NT), :Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC], Teoria de Galois, Galois, Teoria de, Curves, Elliptic Curves, Elliptic, Teoria de, Mathematics - Number Theory, Corbes el·líptiques, 11G05, 11F80, Curves, Elliptic, Galois Representation, :11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) [Classificació AMS], Galois, Arithmetical algebraic geometry, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres, Discontinuous groups

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