Criteria for irreducibility of mod \(p\) representations of Frey curves

DOI10.5802/JTNB.894zbMath1416.11080arXiv1309.4748OpenAlexW2963258780MaRDI QIDQ259493

Nuno Freitas, Samir Siksek

Publication date: 11 March 2016

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.4748

zbMATH Keywords

Fermat-type equationsFrey curvesGalois number field

Mathematics Subject Classification ID

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

Related Items (17)

On the generalized Fermat equation over totally real fields ⋮ Fermat’s Last Theorem and modular curves over real quadratic fields ⋮ On elliptic curves with p-isogenies over quadratic fields ⋮ On some generalized Fermat equations of the form x2+y2n=zp$x^2+y^{2n} = z^p$ ⋮ Asymptotic Fermat for signatures \((r,r,p)\) using the modular approach ⋮ Asymptotic Fermat for signatures (p,p,2)$(p,p,2)$ and (p,p,3)$(p,p,3)$ over totally real fields ⋮ A result on the equation $x^p + y^p = z^r$ using Frey abelian varieties ⋮ \(\mathbb{Q}\)-curves, Hecke characters, and some Diophantine equations. II ⋮ On the solutions of $x^p+y^p=2^rz^p$, $x^p+y^p=z^2$ over totally real fields ⋮ On the finiteness of perfect powers in elliptic divisibility sequences ⋮ Shifted powers in binary recurrence sequences ⋮ A multi-Frey approach to Fermat equations of signature $(r,r,p)$ ⋮ On Serre's uniformity conjecture for semistable elliptic curves over totally real fields ⋮ Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields ⋮ The Generalized Fermat Equation ⋮ Shifted powers in Lucas-Lehmer sequences ⋮ Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\)

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