Q-curves, Hecke characters and some Diophantine equations II
In the article [25] a general procedure to study solutions of the equations x4 − dy2 = zp was presented for negative values of d. The purpose of the present article is to extend our previous results to positive values of d. On doing so, we give a description of the extension Q(√d, √ε)/Q(√d) (where ε...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/226051 |
| Acceso en línea: | http://hdl.handle.net/11336/226051 |
| Access Level: | acceso abierto |
| Palabra clave: | DIOPHANTINE EQUATIONS Q-CURVES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In the article [25] a general procedure to study solutions of the equations x4 − dy2 = zp was presented for negative values of d. The purpose of the present article is to extend our previous results to positive values of d. On doing so, we give a description of the extension Q(√d, √ε)/Q(√d) (where ε is a fundamental unit) needed to prove the existence of a Hecke character over Q(√d) with prescribed local conditions. We also extend some “large image” results due to Ellenberg regarding images of Galois representations coming from Q-curves from imaginary to real quadratic fields. |
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