[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 44 (1002ﾚｽ)
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485(3): 現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/27(月)14:18 ID:yKFtCO8V(4/7) AAS
>>484
つづき
Examples
・More generally, let C be an algebraically closed field and x a variable. Then the absolute Galois group of K = C(x) is free of rank equal to the cardinality of C. This result is due to David Harbater and Florian Pop, and was also proved later by Dan Haran and Moshe Jarden using algebraic methods.[2][3][4]
・Let K be a finite extension of the p-adic numbers Qp. For p ≠ 2, its absolute Galois group is generated by [K:Qp] + 3 elements and has an explicit description by generators and relations. This is a result of Uwe Jannsen and Kay Wingberg.[5][6] Some results are known in the case p = 2, but the structure for Q2 is not known.[7]
Problems
・No direct description is known for the absolute Galois group of the rational numbers. In this case, it follows from Belyi's theorem that the absolute Galois group has a faithful action on the dessins d'enfants of Grothendieck (maps on surfaces), enabling us to "see" the Galois theory of algebraic number fields.
省8
488(1): 現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/27(月)16:33 ID:yKFtCO8V(5/7) AAS
>>487
同意です
>>486
>引用で何が言いたいのかわからんが、要するに他の根拠はないってことか
言いたいこと：必要十分だと（＾＾；
Fierce Inertia saysの ”Jannsen-Wingberg theorem”は
（>>485） Let K be a finite extension of the p-adic numbers Qp. For p ≠ 2, its absolute Galois group is generated by [K:Qp] + 3 elements and has an explicit description by generators and relations. This is a result of Uwe Jannsen and Kay Wingberg.[5][6]
省9
490(2): 2020/04/27(月)17:47 ID:KIlC6vob(3/5) AAS
>>488
どこがどう「範囲外」になるのか、日本語でハッキリ示してみて
ちなみに、Fierce Inertiaの指摘は、
>1. Statements of the form “(Thing X / Property Y) depends only on the absolute Galois group of a p-adic field.”
>
>None of these are surprising or difficult: they all follow from basic class field theory or from the Jannsen-Wingberg theorem (which IS a difficult result, cf. here for a nice overview: 外部ﾘﾝｸ:www.numdam.org
にあるように、"absolute Galois group of a p-adic field"の話でしょ？
省4
492(1): 現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/27(月)18:05 ID:yKFtCO8V(7/7) AAS
>>490
＞どこがどう「範囲外」になるのか、日本語でハッキリ示してみて
DeepL 翻訳使ってみて
外部ﾘﾝｸ:www.deepl.com
そして、分かる範囲で良いから、読んでみて
その方が、今後のためでもあると思うよ
（私の説明なんか、あんまり信用しないようにｗ（＾＾； ）
省16
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