Fermat’s Last Theorem and modular curves over real quadratic fields

DOI10.4064/aa210812-2-4zbMath1503.11071arXiv2102.11699OpenAlexW3196330275MaRDI QIDQ5093862

Philippe Michaud-Jacobs

Publication date: 1 August 2022

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.11699

zbMATH Keywords

modular curvesHilbert modular formsFermat's last theoremGalois representationsirreducibilityFermat equationquadratic pointsFrey curve

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18) Higher degree equations; Fermat's equation (11D41)

Related Items (7)

On elliptic curves with p-isogenies over quadratic fields ⋮ On some generalized Fermat equations of the form x2+y2n=zp$x^2+y^{2n} = z^p$ ⋮ \(\mathbb{Q}\)-curves and the Lebesgue-Nagell equation ⋮ \(\mathbb{Q}\)-curves, Hecke characters, and some Diophantine equations. II ⋮ Cyclic isogenies of elliptic curves over fixed quadratic fields ⋮ COMPUTING POINTS ON BIELLIPTIC MODULAR CURVES OVER FIXED QUADRATIC FIELDS ⋮ Computing quadratic points on modular curves 𝑋₀(𝑁)

Uses Software

• Magma
• SageMath

Cites Work

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