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 classi...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2011 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/96600 |
| Online Access: | https://hdl.handle.net/2445/96600 |
| Access Level: | Open access |
| Keyword: | Corbes el·líptiques Teoria de Galois Geometria algebraica aritmètica Grups discontinus Elliptic curves Galois theory Arithmetical algebraic geometry Discontinuous groups |
| Summary: | 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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