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• Modularity_theorem abstract "In mathematics, the modularity theorem (formerly called the Taniyama–Shimura–Weil conjecture and several related names) states that elliptic curves over the field of rational numbers are related to modular forms. Andrew Wiles proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's last theorem. Later, Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor extended Wiles' techniques to prove the full modularity theorem in 2001. The modularity theorem is a special case of more general conjectures due to Robert Langlands. The Langlands program seeks to attach an automorphic form or automorphic representation (a suitable generalization of a modular form) to more general objects of arithmetic algebraic geometry, such as to every elliptic curve over a number field. Most cases of these extended conjectures have not yet been proved. However, Freitas, Hung & Siksek (2015) proved that elliptic curves defined over real quadratic fields are modular.".
• Modularity_theorem wikiPageExternalLink books?id=Va-quzVwtMsC.
• Modularity_theorem wikiPageExternalLink comm-darmon.pdf.
• Modularity_theorem wikiPageID "174475".
• Modularity_theorem wikiPageLength "12235".
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• Modularity_theorem wikiPageWikiLink Abelian_variety.
• Modularity_theorem wikiPageWikiLink Algebraic_number_field.
• Modularity_theorem wikiPageWikiLink American_Mathematical_Monthly.
• Modularity_theorem wikiPageWikiLink Andrew_Wiles.
• Modularity_theorem wikiPageWikiLink Annals_of_Mathematics.
• Modularity_theorem wikiPageWikiLink Atkin–Lehner_theory.
• Modularity_theorem wikiPageWikiLink Automorphic_form.
• Modularity_theorem wikiPageWikiLink Brian_Conrad.
• Modularity_theorem wikiPageWikiLink Category:Algebraic_curves.
• Modularity_theorem wikiPageWikiLink Category:Conjectures_which_were_proven.
• Modularity_theorem wikiPageWikiLink Category:Modular_forms.
• Modularity_theorem wikiPageWikiLink Category:Riemann_surfaces.
• Modularity_theorem wikiPageWikiLink Category:Theorems_in_algebraic_geometry.
• Modularity_theorem wikiPageWikiLink Category:Theorems_in_number_theory.
• Modularity_theorem wikiPageWikiLink Christophe_Breuil.
• Modularity_theorem wikiPageWikiLink Classical_modular_curve.
• Modularity_theorem wikiPageWikiLink Coefficient.
• Modularity_theorem wikiPageWikiLink Conductor_of_an_elliptic_curve.
• Modularity_theorem wikiPageWikiLink Coprime_integers.
• Modularity_theorem wikiPageWikiLink Cusp_form.
• Modularity_theorem wikiPageWikiLink Differential_of_the_first_kind.
• Modularity_theorem wikiPageWikiLink Dirichlet_series.
• Modularity_theorem wikiPageWikiLink Duke_Mathematical_Journal.
• Modularity_theorem wikiPageWikiLink Elliptic_curve.
• Modularity_theorem wikiPageWikiLink Fermats_Last_Theorem.
• Modularity_theorem wikiPageWikiLink Fourier_series.
• Modularity_theorem wikiPageWikiLink Fred_Diamond.
• Modularity_theorem wikiPageWikiLink Generating_function.
• Modularity_theorem wikiPageWikiLink Goro_Shimura.
• Modularity_theorem wikiPageWikiLink Hasse–Weil_zeta_function.
• Modularity_theorem wikiPageWikiLink Hecke_operator.
• Modularity_theorem wikiPageWikiLink Integer.
• Modularity_theorem wikiPageWikiLink Inventiones_Mathematicae.
• Modularity_theorem wikiPageWikiLink John_H._Coates.
• Modularity_theorem wikiPageWikiLink Journal_of_the_American_Mathematical_Society.
• Modularity_theorem wikiPageWikiLink Langlands_program.
• Modularity_theorem wikiPageWikiLink Leonhard_Euler.
• Modularity_theorem wikiPageWikiLink Mathematics.
• Modularity_theorem wikiPageWikiLink Mathematische_Annalen.
• Modularity_theorem wikiPageWikiLink Modular_form.
• Modularity_theorem wikiPageWikiLink Notices_of_the_American_Mathematical_Society.
• Modularity_theorem wikiPageWikiLink Rational_mapping.
• Modularity_theorem wikiPageWikiLink Rational_number.
• Modularity_theorem wikiPageWikiLink Ribets_theorem.
• Modularity_theorem wikiPageWikiLink Richard_Taylor_(mathematician).
• Modularity_theorem wikiPageWikiLink Robert_Langlands.
• Modularity_theorem wikiPageWikiLink Semistable_abelian_variety.
• Modularity_theorem wikiPageWikiLink Springer_Science+Business_Media.
• Modularity_theorem wikiPageWikiLink Theorem.
• Modularity_theorem wikiPageWikiLinkText "Modularity theorem".
• Modularity_theorem wikiPageWikiLinkText "Shimura-Taniyama-Weil conjecture".
• Modularity_theorem wikiPageWikiLinkText "Shimura–Taniyama conjecture".
• Modularity_theorem wikiPageWikiLinkText "Shimura–Taniyama–Weil conjecture".
• Modularity_theorem wikiPageWikiLinkText "Taniyama-Shimura conjecture".
• Modularity_theorem wikiPageWikiLinkText "Taniyama-Shimura-Weil conjecture".
• Modularity_theorem wikiPageWikiLinkText "Taniyama–Shimura conjecture".
• Modularity_theorem wikiPageWikiLinkText "Taniyama–Shimura-Weil conjecture".
• Modularity_theorem wikiPageWikiLinkText "Taniyama–Shimura–Weil conjecture".
• Modularity_theorem wikiPageWikiLinkText "all elliptic curves defined over the rational numbers are modular".
• Modularity_theorem wikiPageWikiLinkText "modularity theorem".
• Modularity_theorem first "H.".
• Modularity_theorem id "S/s120140".
• Modularity_theorem last "Darmon".
• Modularity_theorem title "Shimura–Taniyama conjecture".
• Modularity_theorem title "Taniyama-Shimura Conjecture".
• Modularity_theorem urlname "Taniyama-ShimuraConjecture".
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• Modularity_theorem subject Category:Algebraic_curves.
• Modularity_theorem subject Category:Conjectures_which_were_proven.
• Modularity_theorem subject Category:Modular_forms.
• Modularity_theorem subject Category:Riemann_surfaces.
• Modularity_theorem subject Category:Theorems_in_algebraic_geometry.
• Modularity_theorem subject Category:Theorems_in_number_theory.
• Modularity_theorem type Conjecture.
• Modularity_theorem type Diacritic.
• Modularity_theorem type Redirect.
• Modularity_theorem type Statement.
• Modularity_theorem type Surface.
• Modularity_theorem type Theorem.
• Modularity_theorem type Variety.
• Modularity_theorem type Statement.
• Modularity_theorem comment "In mathematics, the modularity theorem (formerly called the Taniyama–Shimura–Weil conjecture and several related names) states that elliptic curves over the field of rational numbers are related to modular forms. Andrew Wiles proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's last theorem. Later, Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor extended Wiles' techniques to prove the full modularity theorem in 2001.".
• Modularity_theorem label "Modularity theorem".
• Modularity_theorem sameAs Q649469.
• Modularity_theorem sameAs مبرهنة_النمطية.

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