Asymptotic Fermat for signature \((4, 2, p)\) over number fields

DOI10.1016/j.jnt.2023.03.006arXiv2209.09153OpenAlexW4366767040MaRDI QIDQ6101540

Lucas Villagra Torcomian

Publication date: 1 June 2023

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

Full work available at URL: https://arxiv.org/abs/2209.09153

zbMATH Keywords

Galois representationFermat equationsmodular method

Mathematics Subject Classification ID

Galois representations (11F80) Higher degree equations; Fermat's equation (11D41)

Related Items

Asymptotic Fermat for signatures \((r,r,p)\) using the modular approach

Cites Work

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• A note on class numbers of algebraic number fields
• Finiteness theorems for abelian varieties over number fields.
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Galois properties of torsion points on abelian varieties
• On the asymptotic Fermat's last theorem over number fields
• On 2-class field towers of imaginary quadratic number fields
• Modular elliptic curves and Fermat's Last Theorem
• Elliptic curves over \(\mathbb{Q}_\infty\) are modular
• Class field theory, Diophantine analysis and the asymptotic Fermat's last theorem
• Elliptic curves over real quadratic fields are modular
• The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields
• On the generalized Fermat equation over totally real fields
• Solving Fermat-type equations via modular ℚ-curves over polyquadratic fields
• Galois representations attached to Q-curves and the generalized Fermat equation A 4 + B 2 = C p
• On the Equations z^m = F (x, y ) and Ax^p + By^q = Cz^r
• On ternary Diophantine equations of signature(p,p,2)over number fields
• ℚ-Curves, Hecke characters and some Diophantine equations
• Asymptotic generalized Fermat’s last theorem over number fields
• Heights of Heegner points on Shimura curves.