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Ribet's theorem (earlier called the epsilon conjecture or ε-conjecture) is part of number theory. It concerns properties of Galois representations associated with modular forms. It was proposed by Jean-Pierre Serre and proven by Ken Ribet. The proof was a significant step towards the proof of Fermat's Last Theorem (FLT). As shown by Serre and Ribet, the Taniyama–Shimura conjecture (whose status was unresolved at the time) and the epsilon conjecture together imply that FLT is true.

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rdfs:label	مبرهنة ريبيه (ar) Teorema de Ribet (es) Ribet's theorem (en) Ribets sats (sv) Ε-猜想 (zh)
rdfs:comment	في الرياضيات، مبرهنة ريبيه (المسماة سابقا حدسية إيبسيلون أو حدسية ε) هي نص في نظرية الأعداد يتعلق المرتبطة بالأشكال النمطية. حدسها جان-بيير سير وبرهن عليها . كان البرهان على حدسية إيبسيلون خطوة مهمة نحو البرهان على مبرهنة فيرما الأخيرة. بين سير و ريبيت على أن البرهان على حدسية تانياما-شيمورا وحدسية إيبسيلون معًا يتمم البرهان على مبرهنة فيرما الأخيرة. في ذلك الوقت، لم تكن حدسية تانياما-شيمورا قد حلحلت بعد. (ar) En matemáticas, el teorema de Ribet (antes llamado conjetura épsilon o conjetura ε de Serre) es un enunciado en teoría de números relativo a las propiedades de las representaciones de Galois asociadas a las formas modulares. Fue propuesto por Jean-Pierre Serre y demostrado por Ken Ribet. La prueba de la conjetura epsilon fue un paso significativo hacia la demostración del Último Teorema de Fermat. Como demostraron Serre y Ribet, la conjetura de Taniyama-Shimura (cuya situación no estaba resuelta en ese momento) y la conjetura epsilon, ambas en conjunto, implican que el último teorema de Fermat es cierto. (es) Inom matematiken är Ribets sats (tidigare känd som epsilonförmodan eller ε-förmodan) ett resultat inom talteori om egenskaper av Galoisrepresentationer associerade med modulära former. Förmodan framlades av Jean-Pierre Serre och bevisades av Ken Ribet. Beviset av epsilonförmodan var ett viktigt steg mot beviset av Fermats stora sats. Såsom bevisat av Serre och Ribet, följer Fermats stora sats ur Taniyama–Shimuras sats (som då ännu var obevisad) och epsilonförmodan. (sv) 在数学中，Ribet定理（英語：Ribet's theorem，以前稱為ε猜想）是數論中關於與模形式相關的性質的陳述。它由讓-皮埃爾·塞爾提出並由肯尼斯·阿蘭·黎貝證明。ε猜想的證明是證明費馬大定理的重要一步。如Serre和Ribet所示，谷山－志村定理（當時未解決的狀態）和ε猜想意味著費馬大定理是正確的。在數學術語中，Ribet定理表明，如果與橢圓曲線相關的伽羅瓦表示具有某些特性，那麼該曲線不能是模形式的（在不存在產生相同伽羅瓦表示的模形式的意義上）。 (zh) Ribet's theorem (earlier called the epsilon conjecture or ε-conjecture) is part of number theory. It concerns properties of Galois representations associated with modular forms. It was proposed by Jean-Pierre Serre and proven by Ken Ribet. The proof was a significant step towards the proof of Fermat's Last Theorem (FLT). As shown by Serre and Ribet, the Taniyama–Shimura conjecture (whose status was unresolved at the time) and the epsilon conjecture together imply that FLT is true. (en)
dcterms:subject	Fermat's Last Theorem Modular forms Riemann surfaces Theorems in number theory Theorems in algebraic geometry Algebraic curves
Wikipage page ID	700981 (xsd:integer)
Wikipage revision ID	1084982770 (xsd:integer)
Link from a Wikipage to another Wikipage	Barry Mazur Fermat's Last Theorem Modular forms Richard Taylor (mathematician) Descent (mathematics) Riemann surfaces Theorems in number theory Elliptic curve Gerhard Frey Modular form Modularity theorem Conductor of an elliptic curve Yutaka Taniyama Frey curve Abc conjecture Fermat's Last Theorem Fourier series Number theory Mathematical proof Radical of an integer Atkin–Lehner theory Isogeny Jean-Pierre Serre Theorems in algebraic geometry Abelian variety Algebraic curves Ken Ribet Kenneth Alan Ribet Kevin Buzzard Discriminant Pierre de Fermat Wiles' proof of Fermat's Last Theorem Tate curve Taniyama–Shimura conjecture Galois representation
Link from a Wikipage to an external page	http://mathworld.wolfram.com/FreyCurve.html http://mathworld.wolfram.com/RibetsTheorem.html http://www.msri.org/communications/vmath/VMathVideos/VideoInfo/3830/show_video http://www.numdam.org/item%3Fid=AFST_1990_5_11_1_116_0 http://math.stanford.edu/~lekheng/flt/taylor-wiles.pdf http://math.stanford.edu/~lekheng/flt/wiles.pdf
sameAs	Ribet's theorem Ribet's theorem Ribet's theorem Ribet's theorem Ribet's theorem Ribet's theorem Ribet's theorem Ribet's theorem Ribet's theorem Ribet's theorem
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