Home > Articles > Published articles > Q-curves, Hecke characters and some Diophantine equations II |
Date: | 2023 |
Abstract: | 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. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Subject: | Q-curves ; Diophantine equations |
Published in: | Publicacions matemàtiques, Vol. 67 Núm. 2 (2023) , p. 569-599 (Articles) , ISSN 2014-4350 |
31 p, 476.1 KB |