The generalized Fermat equation with exponents 2, 3,

DOI10.1112/S0010437X19007693zbMath1450.11024arXiv1703.05058OpenAlexW2989807380WikidataQ126662284 ScholiaQ126662284MaRDI QIDQ5203821

Bartosz Naskręcki, Michael Stoll, Nuno Freitas

Publication date: 9 December 2019

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.05058

zbMATH Keywords

rational pointsmodularitySelmer groupsymplectic methodgeneralized Fermat equationChabauty

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Galois representations (11F80) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Higher degree equations; Fermat's equation (11D41) Global ground fields in algebraic geometry (14G25) Elliptic curves over local fields (11G07)

Related Items (4)

On the symplectic type of isomorphisms of the 𝑝-torsion of elliptic curves ⋮ Diophantine equations with three monomials ⋮ AN APPLICATION OF THE MODULAR METHOD AND THE SYMPLECTIC ARGUMENT TO A LEBESGUE–NAGELL EQUATION ⋮ On a class of generalized Fermat equations of signature \((2,2n,3)\)

Uses Software

• Magma
• ecdata

Cites Work

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• On the Fermat-type equation \(x^3+y^3=z^p\)
• Explicit Chabauty over number fields
• Rational points on \(X_0^+(p^r)\)
• The automorphism group of the non-split Cartan modular curve of level 11
• Sums of two cubes as twisted perfect powers, revisited
• An exceptional isomorphism between modular curves of level 13
• Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\)
• On the failure of semistability of elliptic curves with additive reduction
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• The Magma algebra system. I: The user language
• On a result of Imin Chen
• Explicit Chabauty-Kim for the split Cartan modular curve of level 13
• Fermat's last theorem over some small real quadratic fields
• The generalised Fermat equation \(x^{2} + y^{3} = z^{15}\)
• Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen
• Good reduction of abelian varieties
• The primitive solutions to \(x^3+y^9=z^2\)
• An application of the symplectic argument to some Fermat-type equations
• Implementing 2-descent for Jacobians of hyperelliptic curves
• GENERALIZED EXPLICIT DESCENT AND ITS APPLICATION TO CURVES OF GENUS 3
• On families of 7- and 11-congruent elliptic curves
• On the change of root numbers under twisting and applications
• Two-cover descent on hyperelliptic curves
• The Mordell–Weil sieve: proving non-existence of rational points on curves
• Primitive Integral Solutions to x2+y3=z10
• Root numbers of elliptic curves in residue characteristic 2
• The Arithmetic of Elliptic Curves
• The Jacobians of Non-Split Cartan Modular Curves
• Chabauty methods using elliptic curves
• Courbes de Fermat: résultats et problèmes
• Chabauty Without the Mordell-Weil Group
• A complete solution to X2 + Y3 + Z5 = 0
• On the Equations z^m = F (x, y ) and Ax^p + By^q = Cz^r
• On the symplectic type of isomorphisms of the 𝑝-torsion of elliptic curves
• On the computation of local components of a newform
• Erratum: “On the computation of local components of a newform”
• Integral Tate modules and splitting of primes in torsion fields of elliptic curves
• Number Theory
• On a question of B. Mazur

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