Modularity of elliptic curves over abelian totally real fields unramified at 3, 5, and 7

DOI10.5802/jtnb.1047zbMath1441.11135arXiv1606.06597OpenAlexW2963687542WikidataQ128016402 ScholiaQ128016402MaRDI QIDQ5223363

Sho Yoshikawa

Publication date: 17 July 2019

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

Full work available at URL: https://arxiv.org/abs/1606.06597

zbMATH Keywords

elliptic curvesHilbert modular formsGalois 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 (2)

Reducible mod 105 representations and modularity of elliptic curves ⋮ The modularity of elliptic curves over all but finitely many totally real fields of degree 5

Cites Work

• Unnamed Item
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• Residually reducible representations and modular forms
• Nearly ordinary deformations of irreducible residual representations
• Remarks on automorphy of residually dihedral representations
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\)
• Elliptic curves over real quadratic fields are modular
• Good reduction of abelian varieties
• Automorphy of some residually dihedral Galois representations
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Potential modularity – a survey
• Modularity of nearly ordinary 2-adic residually dihedral Galois representations
• On the parity of ranks of Selmer groups IV. With an appendix by Jean-Pierre Wintenberger
• REMARKS ON A CONJECTURE OF FONTAINE AND MAZUR

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