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

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 ca...

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Veröffentlicht in:	Proceedings of the American Mathematical Society 2011-06, Vol.139 (6), p.1961-1969
Hauptverfasser:	DIEULEFAIT, LUIS, GONZÁLEZ-JIMÉNEZ, ENRIQUE, URROZ, JORGE JIMÉNEZ
Format:	Artikel
Sprache:	eng
Schlagworte:	11 Number theory 11F Discontinuous groups and automorphic forms 11G Arithmetic algebraic geometry (Diophantine geometry) Algebra Algebraic geometry Classificació AMS Corbes el·líptiques Curves Curves, Elliptic Exact sciences and technology Factorization Galois theory Galois, Teoria de General mathematics General, history and biography Information representations Integers Matemàtiques i estadística Mathematical tables Mathematics Number theory Polynomials Prime numbers Sciences and techniques of general use Teoria de nombres Torsion Torsió Àlgebra Àrees temàtiques de la UPC
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Zusammenfassung:	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.
ISSN:	0002-9939 1088-6826
DOI:	10.1090/S0002-9939-2010-10621-4