Proving Modularity for a given elliptic curve over an imaginary quadratic field
We present an algorithm to determine if the L-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and Berger-Harcos (cf. [HST93], [Tay94] and [BH07]) we can associate to an...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2010 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/15075 |
| Acesso em linha: | http://hdl.handle.net/11336/15075 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Elliptic curves Modularity https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | We present an algorithm to determine if the L-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and Berger-Harcos (cf. [HST93], [Tay94] and [BH07]) we can associate to an automorphic representation a family of compatible ℓ-adic representations. Our algorithm is based on Faltings-Serre’s method to prove that ℓ-adic Galois representations are isomorphic. Using the algorithm we provide the first examples of modular elliptic curves over imaginary quadratic fields with residual 2-adic image isomorphic to S3 and C3. |
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