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Title: On fields of definition of torsion points of elliptic curves with complex multiplication
Author: Dieulefait, L. V. (Luis Victor)
Gonzalez-Jimenez, Enrique
Jimenez Urroz, Jorge
Keywords: Corbes el·líptiques
Teoria de Galois
Geometria algebraica aritmètica
Grups discontinus
Elliptic curves
Galois theory
Arithmetical algebraic geometry
Discontinuous groups
Issue Date: Jun-2011
Publisher: American Mathematical Society (AMS)
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.
Note: Reproducció del document publicat a:
It is part of: Proceedings of the American Mathematical Society, 2011, vol. 139, num. 6, p. 1961-1969
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ISSN: 0002-9939
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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