翻訳と辞書 Words near each other ・ Ribosomal protein L4 ・ Ribosomal protein L5 ・ Ribosomal protein leader ・ Ribes thacherianum ・ Ribes triste ・ Ribes tularense ・ Ribes velutinum ・ Ribes viburnifolium ・ Ribes victoris ・ Ribes viscosissimum ・ Ribes watsonianum ・ Ribes wolfii ・ Ribes, Ardèche ・ Ribesalbes ・ Ribet Academy ・ Ribet's theorem ・ Ribeyre Island ・ Ribeyret ・ Ribeyro ・ Ribeyrolle 1918 automatic carbine ・ Ribfest ・ Ribhus ・ Ribicioara River ・ Ribier, California ・ Ribiers ・ Ribino ・ Ribisi ・ Ribitol ・ Ribitol 2-dehydrogenase ・ Ribitol-5-phosphate 2-dehydrogenase Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Ribet's theorem ： ウィキペディア英語版 Ribet's theorem In mathematics, Ribet's theorem (earlier called the epsilon conjecture or ε-conjecture) is a statement in number theory concerning properties of Galois representations associated with modular forms. It was proposed by Jean-Pierre Serre and proved by Ken Ribet. The proof of the epsilon conjecture was a significant step towards the proof of Fermat's Last Theorem. As shown by Serre and Ribet, the Taniyama–Shimura conjecture (whose status was unresolved at the time) and the epsilon conjecture together imply that Fermat's Last Theorem is true. == Statement == Let ''f'' be a weight 2 newform on Γ0(''qN'')–i.e. of level ''qN'' where ''q'' does not divide ''N''–with absolutely irreducible 2-dimensional mod ''p'' Galois representation ''ρf,p'' unramified at ''q'' if ''q ≠ p'' and finite flat at ''q = p''. Then there exists a weight 2 newform ''g'' of level ''N'' such that :$\backslash rho\_\; \backslash simeq\; \backslash rho\_.$ In particular, if ''E'' is an elliptic curve over $\backslash mathbb$ with conductor ''qN'', then the Modularity theorem guarantees that there exists a weight 2 newform ''f'' of level ''qN'' such that the 2-dimensional mod ''p'' Galois representation ''ρf, p'' of ''f'' is isomorphic to the 2-dimensional mod ''p'' Galois representation ''ρE, p'' of ''E''. To apply Ribet's Theorem to ''ρE, p'', it suffices to check the irreducibility and ramification of ''ρE, p''. Using the theory of the Tate curve, one can prove that ''ρE, p'' is unramified at ''q ≠ p'' and finite flat at ''q = p'' if ''p'' divides the power to which ''q'' appears in the minimal discriminant ''ΔE''. Then Ribet's theorem implies that there exists a weight 2 newform ''g'' of level ''N'' such that ''ρg, p ≈ ρE, p''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ribet's theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.