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The '''Taniyama-Shimura theorem''' establishes an important connection between [[elliptic curve]]s, which are objects from [[algebraic geometry]], and [[modular form]]s, which are certain periodic [[holomorphic function]]s investigated in [[number theory]]. Despite the name, which was a carry over from the Taniyama-Shimura ''[[conjecture]]'', the theorem is the work of [[Andrew Wiles]], [[Christophe Breuil]], [[Brian Conrad]], [[Fred Diamond]], and [[Richard Taylor (mathematician)|Richard Taylor]].
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* Henri Darmon: ''[http://www.ams.org/notices/199911/comm-darmon.pdf A Proof of the Full Shimura-Taniyama-Weil Conjecture Is Announced]'', Notices of the American Mathematical Society, Vol. 46 (1999), No. 11. Contains a gentle introduction to the theorem and an outline of the proof.
* Brian Conrad, Fred Diamond, Richard Taylor: ''Modularity of certain potentially Barsotti-Tate Galois representations'', Journal of the American Mathematical Society 12 (1999), pp. 521–567. Contains the proof.
[[Category:Algebraic curves]]
[[Category:Riemann surfaces]]
[[Category:Modular forms]]
[[Category:Theorems]]
[[ja:谷山－志村予想]]
[[he:השערת טניאמה-שימורה]]
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