Q-curves, Hecke characters and some Diophantine equations II
Pacetti, Ariel (Universidade de Aveiro. Departamento de Matemática)

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.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Q-curves ; Diophantine equations
Published in:	Publicacions matemàtiques, Vol. 67, Num. 2 (2023) , p. 569-569-599 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/418409
DOI: 10.5565/PUBLMAT6722304

31 p, 476.1 KB

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