Modularity theorem: Difference between revisions

Revision as of 09:27, 7 March 2024

Revision as of 09:27, 7 March 2024

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{{Short description|Relates rational elliptic curves to modular forms}}

*[[{{Distinguish|Serre's modularity conjecture]]}}

<!--{{no footnotes|date=January 2021}}Harvard style footnotes converted to short footnotes-->

{{Infobox mathematical statement

| name = Modularity theorem

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cannot be modular.{{sfn|Ribet|1990}} Thus, the proof of the Taniyama–Shimura–Weil conjecture for this family of elliptic curves (called Hellegouarch–Frey curves) implies FLT. The proof of the link between these two statements, based on an idea of [[Gerhard Frey]] (1985), is difficult and technical. It was established by [[Kenneth Ribet]] in 1987.<ref>See the survey of {{cite journal |first=K. |last=Ribet |title=From the Taniyama–Shimura conjecture to Fermat's Last Theorem |journal=Annales de la Faculté des Sciences de Toulouse |volume=11 |year=1990b |pages=116–139 |doi= 10.5802/afst.698|url=http://www.numdam.org/item?id=AFST_1990_5_11_1_116_0 |doi-access=free }}</ref>

== See also ==

*[[Serre's modularity conjecture]]

==Notes==