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...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2011 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/12251 |
| Acesso em linha: | https://hdl.handle.net/2117/12251 https://dx.doi.org/10.1090/S0002-9939-2010-10621-4 |
| Access Level: | Acceso aberto |
| Palavra-chave: | 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) Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
| Resumo: | 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. |
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