Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields

DOI10.1142/S1793042121500585zbMath1477.11109arXiv2004.07611MaRDI QIDQ3382982

George C. Ţurcaş, Filip Najman

Publication date: 23 September 2021

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07611

zbMATH Keywords

elliptic curvesGalois representationsFermat equation

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Galois representations (11F80)

Related Items (4)

Fermat’s Last Theorem and modular curves over real quadratic fields ⋮ On some generalized Fermat equations of the form x2+y2n=zp$x^2+y^{2n} = z^p$ ⋮ \(\mathbb{Q}\)-curves, Hecke characters, and some Diophantine equations. II ⋮ On ternary Diophantine equations of signature(p,p,2)over number fields

Cites Work

• Unnamed Item
• Criteria for irreducibility of mod \(p\) representations of Frey curves
• Quelques applications du théorème de densité de Chebotarev
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Modular curves and the Eisenstein ideal
• On the asymptotic Fermat's last theorem over number fields
• Torsion points on elliptic curves and \(q\)-coefficients of modular forms
• Bounds for the torsion of elliptic curves over number fields
• On Serre's modularity conjecture and Fermat's equation over quadratic imaginary fields of class number one
• Class field theory, Diophantine analysis and the asymptotic Fermat's last theorem
• On Fermat's equation over some quadratic imaginary number fields
• Galois properties of points of finite order of elliptic curves
• Rational points of Abelian varieties with values in towers of number fields
• Hyperelliptic modular curves and isogenies of elliptic curves over quadratic fields
• The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields
• Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres
• Les Schémas de Modules de Courbes Elliptiques
• Asymptotic generalized Fermat’s last theorem over number fields
• Determinants of subquotients of Galois representations associated with abelian varieties

This page was built for publication: Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields