Concept information
Preferred term
modularity theorem
Definition(s)
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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)
Broader concept(s)
Synonym(s)
- modularity conjecture for elliptic curves
- Taniyama-Shimura conjecture
- Taniyama-Weil conjecture
In other languages
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French
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conjecture de Shimura-Taniyama
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conjecture de Shimura-Taniyama-Weil
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conjecture de Taniyama-Weil
URI
http://data.loterre.fr/ark:/67375/PSR-JC2B70CX-0
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