Parametrization of abelian K-surfaces with quaternionic multiplication
We prove that the Abelian $K$-surfaces whose endomorphism algebra is a rational quaternion algebra are parametrized, up to isogeny, by the $K$-rational points of the quotient of certain Shimura curves by the group of their Atkin-Lehner involutions.
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/193327 |
| Acceso en línea: | https://hdl.handle.net/2445/193327 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometria algebraica aritmètica Varietats abelianes Arithmetical algebraic geometry Abelian varieties |
| Sumario: | We prove that the Abelian $K$-surfaces whose endomorphism algebra is a rational quaternion algebra are parametrized, up to isogeny, by the $K$-rational points of the quotient of certain Shimura curves by the group of their Atkin-Lehner involutions. |
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