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

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Title:	On fields of definition of torsion points of elliptic curves with complex multiplication
Author:	Dieulefait, Luis Victor; Gonzalez Jimenez, Enrique; Jiménez Urroz, Jorge
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
Abstract:	For any elliptic curve E defined over the rationals with complex multiplication (CM) 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.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres -Curves, Elliptic -Torsion -Galois theory -Corbes el·líptiques -Torsió -Galois, Teoria de -Classificació AMS::11 Number theory::11F Discontinuous groups and automorphic forms -Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry)
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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