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Concept information

number > number theory > modularity theorem
geometry > algebraic geometry > algebraic variety > algebraic curve > modularity theorem

Terme préférentiel

modularity theorem  

Définition

  • The modularity theorem (formerly called the Taniyama–Shimura conjecture, Taniyama-Weil conjecture or modularity conjecture for elliptic curves) 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, a series of papers by Wiles's former students Brian Conrad, Fred Diamond and Richard Taylor, culminating in a joint paper with Christophe Breuil, extended Wiles's techniques to prove the full modularity theorem in 2001.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Modularity_theorem)

Concept générique

Synonyme(s)

  • modularity conjecture for elliptic curves
  • Taniyama-Shimura conjecture
  • Taniyama-Weil conjecture

Traductions

  • théorème de modularité

    français

  • conjecture de Shimura-Taniyama
  • conjecture de Shimura-Taniyama-Weil
  • conjecture de Taniyama-Weil

URI

http://data.loterre.fr/ark:/67375/PSR-JC2B70CX-0

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