[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63 (1002ﾚｽ)
上下前次1-新
抽出解除 ﾚｽ栞
このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索 歴削→次ｽﾚ 栞削→次ｽﾚ 過去ﾛｸﾞﾒﾆｭｰ
526(2): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [] 2019/04/15(月) 07:55:04.77 ID:GY+CIXbC(7/18) AAS
>>525
つづき
Grothendieck originally developed etale cohomology in an extremely general setting, working with concepts such as Grothendieck toposes and Grothendieck universes.
With hindsight, much of this machinery proved unnecessary for most practical applications of the etale theory, and Deligne (1977) gave a simplified exposition of etale cohomology theory. Grothendieck's use of these universes
(whose existence cannot be proved in ZFC) led to some uninformed speculation that etale cohomology and its applications (such as the proof of Fermat's last theorem) needed axioms beyond ZFC.
In practice etale cohomology is used mainly for constructible sheaves over schemes of finite type over the integers, and this needs no deep axioms of set theory: with a little care it can be constructed in this case without using any uncountable sets, and this can easily be done in ZFC (and even in much weaker theories).
Etale cohomology quickly found other applications, for example Deligne and Lusztig used it to construct representations of finite groups of Lie type; see Deligne?Lusztig theory.
(引用終り)
以上
527: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [] 2019/04/15(月) 07:57:12.85 ID:GY+CIXbC(8/18) AAS
>>526 付記
(引用開始)
(whose existence cannot be proved in ZFC) led to some uninformed speculation that etale cohomology and its applications (such as the proof of Fermat's last theorem) needed axioms beyond ZFC.
In practice etale cohomology is used mainly for constructible sheaves over schemes of finite type over the integers, and this needs no deep axioms of set theory: with a little care it can be constructed in this case without using any uncountable sets, and this can easily be done in ZFC (and even in much weaker theories).
(引用終り)
ここ、けっこう面白いね（＾＾；
564(2): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [] 2019/04/16(火) 10:40:22.74 ID:WM/U/f3d(2/11) AAS
>>526 付記
(引用開始)
(whose existence cannot be proved in ZFC) led to some uninformed speculation that etale cohomology and its applications (such as the proof of Fermat's last theorem) needed axioms beyond ZFC.
In practice etale cohomology is used mainly for constructible sheaves over schemes of finite type over the integers, and this needs no deep axioms of set theory: with a little care it can be constructed in this case without using any uncountable sets, and this can easily be done in ZFC (and even in much weaker theories).
(引用終り)
蛇足だけど
”Grothendieck originally developed etale cohomology in an extremely general setting, working with concepts such as Grothendieck toposes and Grothendieck universes.
In practice etale cohomology is used mainly for constructible sheaves over schemes of finite type over the integers, and this needs no deep axioms of set theory: with a little care it can be constructed in this case without using any uncountable sets, and this can easily be done in ZFC (and even in much weaker theories).
Etale cohomology quickly found other applications, for example Deligne and Lusztig used it to construct representations of finite groups of Lie type; see Deligne?Lusztig theory.”
ってことで、Grothendieck 先生は、ZFC超えの「Grothendieck toposes and Grothendieck universes」を構想していたんだ
だが、Deligne先生はつまみ食いしたんだ。ZFC内で、簡単に済ました
そこらの確執が、たしか、Grothendieckの伝記みたいなのに書いてあったね（＾＾
上下前次1-新書関写板覧索設栞歴
ｽﾚ情報 赤ﾚｽ抽出 画像ﾚｽ抽出 歴の未読ｽﾚ AAｻﾑﾈｲﾙ
ぬこの手 ぬこTOP 0.055s