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2011-06

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/96600

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

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http://dx.doi.org/10.1090/S0002-9939-2010-10621-4

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

Corbes el·líptiques, Teoria de Galois, Geometria algebraica aritmètica, Grups discontinus

Subject (English)

Elliptic curves, Galois theory, Arithmetical algebraic geometry, Discontinuous groups

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

DIEULEFAIT, L. V. (Luis Victor), GONZALEZ-JIMENEZ, Enrique and JIMENEZ URROZ, Jorge. On fields of definition of torsion points of elliptic curves with complex multiplication. Proceedings of the American Mathematical Society. 2011. Vol. 139, num. 6, pags. 1961-1969. ISSN 0002-9939. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/96600

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