On the modularity of supersingular elliptic curves over certain totally real number fields

DOI10.1016/j.jnt.2007.10.003zbMath1225.11076arXiv0708.3942OpenAlexW2123022072MaRDI QIDQ2474302

Frazer Jarvis, Jayanta Manoharmayum

Publication date: 5 March 2008

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

Full work available at URL: https://arxiv.org/abs/0708.3942

zbMATH Keywords

supersingular reductionlocal Galois representationsmodularity of elliptic curves over totally real fieldsSerre's conjecture for mod 7 representations

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Galois representations (11F80) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (11)

Elliptic curves over totally real quartic fields not containing √5 are modular ⋮ On Serre's conjecture for mod \(\ell \) Galois representations over totally real fields ⋮ Elliptic curves over totally real cubic fields are modular ⋮ The Fermat equation over \(\mathbb Q(\sqrt 2)\) ⋮ Moduli of finite flat group schemes, and modularity ⋮ Modular elliptic curves over the field of twelfth roots of unity ⋮ Elliptic curves over real quadratic fields are modular ⋮ Solving Fermat-type equations via modular ℚ-curves over polyquadratic fields ⋮ Unnamed Item ⋮ On an elliptic curve defined over $\mathbb {Q}(\sqrt {-23})$ ⋮ Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\)

Uses Software

• ecdata

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric deformations of modular Galois representations
• On Galois representations associated to Hilbert modular forms
• Moduli of finite flat group schemes, and modularity
• The Taylor-Wiles construction and multiplicity one
• Residually reducible representations and modular forms
• On the modularity of certain \(\text{GL}_2(\mathbb{F}_7)\) Galois representations
• Nearly ordinary deformations of irreducible residual representations
• The Fermat equation over \(\mathbb Q(\sqrt 2)\)
• Base change and a problem of Serre
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Ramified deformation problems
• On the meromorphic continuation of degree two \(L\)-functions
• Galois properties of points of finite order of elliptic curves
• On icosahedral Artin representations, II
• Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert

This page was built for publication: On the modularity of supersingular elliptic curves over certain totally real number fields