[過去ﾛｸﾞ] Interｰuniversal geometryとABC予想(応用スレ)51 (1002ﾚｽ)
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418(2): 2021/02/13(土)18:17 ID:wXktx3pj(9/18) AAS
>>375 より
>エタール基本群 Etale fundamental group
>(参考)
>外部ﾘﾝｸ:en.wikipedia.org
>Etale fundamental group

(引用開始)
（原文）
省13

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419(2): 2021/02/13(土)18:18 ID:wXktx3pj(10/18) AAS
>>418
つづき

（原文）
Examples and theorems
The most basic example of a fundamental group is π1(Spec k), the fundamental group of a field k. Essentially by definition, the fundamental group of k can be shown to be isomorphic to the absolute Galois group Gal (ksep / k). More precisely, the choice of a geometric point of Spec (k) is equivalent to giving a separably closed extension field K, and the fundamental group with respect to that base point identifies with the Galois group Gal (K / k). This interpretation of the Galois group is known as Grothendieck's Galois theory.

More generally, for any geometrically connected variety X over a field k (i.e., X is such that Xsep := X ×k ksep is connected) there is an exact sequence of profinite groups

1 → π1(Xsep, x) → π1(X, x) → Gal(ksep / k) → 1.
省8

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421: 2021/02/13(土)18:25 ID:4eb0VVkt(18/19) AAS
>>418
エタール束　理解した？
外部ﾘﾝｸ:ja.wikipedia.org

「局所同相写像 E → X は X 上のエタール束とよばれる。」

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