>>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（＾＾
