Q-curves, Hecke characters and some Diophantine equations II
In the article [25] a general procedure to study solutions of the equations x4 - dy2 = z p 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, √e)/Q(√d) (where...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:280942 |
| Acceso en línea: | https://ddd.uab.cat/record/280942 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6722304 |
| Access Level: | acceso abierto |
| Palabra clave: | Q-curves Diophantine equations |
| Sumario: | In the article [25] a general procedure to study solutions of the equations x4 - dy2 = z p 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, √e)/Q(√d) (where e 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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