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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.".
- Modularity_theorem wikiPageExternalLink books?id=Va-quzVwtMsC.
- Modularity_theorem wikiPageExternalLink comm-darmon.pdf.
- Modularity_theorem wikiPageID "174475".
- Modularity_theorem wikiPageRevisionID "606128395".
- Modularity_theorem first "H.".
- Modularity_theorem hasPhotoCollection Modularity_theorem.
- 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".
- Modularity_theorem subject Category:Algebraic_curves.
- 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 Abstraction100002137.
- Modularity_theorem type AlgebraicCurves.
- Modularity_theorem type Attribute100024264.
- Modularity_theorem type Communication100033020.
- Modularity_theorem type Curve113867641.
- Modularity_theorem type Form106290637.
- Modularity_theorem type LanguageUnit106284225.
- Modularity_theorem type Line113863771.
- Modularity_theorem type Message106598915.
- Modularity_theorem type ModularForms.
- Modularity_theorem type Part113809207.
- Modularity_theorem type Proposition106750804.
- Modularity_theorem type Relation100031921.
- Modularity_theorem type Shape100027807.
- Modularity_theorem type Statement106722453.
- Modularity_theorem type Theorem106752293.
- Modularity_theorem type TheoremsInAlgebraicGeometry.
- Modularity_theorem type TheoremsInNumberTheory.
- Modularity_theorem type Word106286395.
- 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 "Conjecture de Shimura-Taniyama-Weil".
- Modularity_theorem label "Modularity theorem".
- Modularity_theorem label "Modularitätssatz".
- Modularity_theorem label "Stelling van Shimura-Taniyama".
- Modularity_theorem label "Teorema de Shimura-Taniyama-Weil".
- Modularity_theorem label "Teorema de Taniyama-Shimura".
- Modularity_theorem label "Teorema di Taniyama-Shimura".
- Modularity_theorem label "Теорема о модулярности".
- Modularity_theorem label "مبرهنة النمطية".
- Modularity_theorem label "谷山志村予想".
- Modularity_theorem label "谷山－志村定理".
- Modularity_theorem sameAs Tanijamova-Šimurova_domněnka.
- Modularity_theorem sameAs Modularitätssatz.
- Modularity_theorem sameAs Θεώρημα_των_Shimura-Taniyama.
- Modularity_theorem sameAs Teorema_de_Taniyama-Shimura.
- Modularity_theorem sameAs Conjecture_de_Shimura-Taniyama-Weil.
- Modularity_theorem sameAs Teorema_di_Taniyama-Shimura.
- Modularity_theorem sameAs 谷山志村予想.
- Modularity_theorem sameAs 모듈러성_정리.
- Modularity_theorem sameAs Stelling_van_Shimura-Taniyama.
- Modularity_theorem sameAs Teorema_de_Shimura-Taniyama-Weil.
- Modularity_theorem sameAs m.017kl9.
- Modularity_theorem sameAs Q649469.
- Modularity_theorem sameAs Q649469.
- Modularity_theorem sameAs Modularity_theorem.
- Modularity_theorem wasDerivedFrom Modularity_theorem?oldid=606128395.
- Modularity_theorem isPrimaryTopicOf Modularity_theorem.