Residual Galois representations of elliptic curves with image contained in the normaliser of a nonsplit Cartan

DOI10.2140/ant.2021.15.747zbMath1479.11097arXiv2002.02714OpenAlexW3005414166MaRDI QIDQ2027517

Samuel Le Fourn, Pedro Lemos

Publication date: 27 May 2021

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.02714

zbMATH Keywords

Galois representations of elliptic curvesnonsplit Cartan subgroupSerre uniformity problem

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18)

Related Items (5)

Quadratic points on bielliptic modular curves ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ Cyclic isogenies of elliptic curves over fixed quadratic fields ⋮ Growth of torsion groups of elliptic curves upon base change from number fields ⋮ Some uniform bounds for elliptic curves over \(\mathbb{Q} \)

Cites Work

• Unnamed Item
• Surjectivity of Galois representations associated with quadratic \(\mathbb {Q}\)-curves
• Rational points on \(X_0^+(p^r)\)
• Serre's uniformity problem in the split Cartan case
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Modular curves and the Eisenstein ideal
• Period theorem and minimal degrees of isogenies
• Galois properties of points of finite order of elliptic curves
• Runge's Method and Modular Curves
• Serre’s uniformity conjecture for elliptic curves with rational cyclic isogenies
• Isogenies of non-CM elliptic curves with rational j-invariants over number fields
• Les Schémas de Modules de Courbes Elliptiques

This page was built for publication: Residual Galois representations of elliptic curves with image contained in the normaliser of a nonsplit Cartan