現代数学の系譜工学物理雑談古典ガロア理論も読む79

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む79 (1002ﾚｽ)
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767: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/12/29(日) 23:08:38.66 ID:uR3g5aDb

>>766
つづき

Following this strategy, a proof of Fermat's Last Theorem required two steps.
First, it was necessary to prove the modularity theorem ? or at least to prove it for the types of elliptical curves that included Frey's equation (known as semistable elliptic curves).
This was widely believed inaccessible to proof by contemporary mathematicians.[121]:203?205, 223, 226
Second, it was necessary to show that Frey's intuition was correct: that if an elliptic curve were constructed in this way, using a set of numbers that were a solution of Fermat's equation, the resulting elliptic curve could not be modular.
Frey showed that this was plausible but did not go as far as giving a full proof.
The missing piece (the so-called "epsilon conjecture", now known as Ribet's theorem) was identified by Jean-Pierre Serre who also gave an almost-complete proof and the link suggested by Frey was finally proved in 1986 by Ken Ribet.[124]
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1573769803/767

768: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/12/29(日) 23:25:31.39 ID:uR3g5aDb

>>767 追加

英文の方が圧倒的に詳しいね
まあ、和文→英文の順に読めば良い（＾＾

（英文）
https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem
Wiles's proof of Fermat's Last Theorem
(抜粋)
Contents
1 Precursors to Wiles' proof
1.1 Fermat's Last Theorem and progress prior to 1980
1.2 The Taniyama?Shimura?Weil conjecture
1.3 Frey's curve
1.4 Ribet's theorem
1.5 Situation prior to Wiles' proof
2 Andrew Wiles
3 Announcement and subsequent developments
3.1 Announcement and final proof (1993?1995)
3.2 Subsequent developments
4 Summary of Wiles' proof
5 Mathematical detail of Wiles proof
5.1 Overview
5.2 General approach and strategy
5.3 3-5 trick
5.4 Structure of Wiles's proof
5.5 Overviews available in the literature
6 References

（和文）
https://ja.wikipedia.org/wiki/%E3%83%AF%E3%82%A4%E3%83%AB%E3%82%BA%E3%81%AB%E3%82%88%E3%82%8B%E3%83%95%E3%82%A7%E3%83%AB%E3%83%9E%E3%83%BC%E3%81%AE%E6%9C%80%E7%B5%82%E5%AE%9A%E7%90%86%E3%81%AE%E8%A8%BC%E6%98%8E
ワイルズによるフェルマーの最終定理の証明
(抜粋)
目次
1 ワイルズの証明以前の進展
1.1 フェルマーの最終定理
1.2 ワイルズ以前の特定の指数に関する部分的な解
1.3 谷山・志村・ヴェイユ予想
1.4 フライ曲線
1.5 フライ曲線を用いたフェルマーの最終定理への挑戦
1.6 リベットの定理
2 アンドリュー・ワイルズ
3 証明の発表とその後の発展
3.1 証明の発表と最終的な証明 (1993?1995)
3.2 その後の発展
4 脚注
5 参考文献
6 外部リンク
6.1 ワイルズの証明の解説

http://rio2016.5ch.net/test/read.cgi/math/1573769803/768

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