[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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376(1): 2021/02/11(木)21:33 ID:xRkvTpwx(20/21) AAS
>>375
つづき

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.

The pro-etale fundamental group
省5

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388(2): 2021/02/12(金)08:00 ID:ON+uWjNc(1/2) AAS
>>371
>数体Fの上に一点抜き楕円曲線X（＝双曲的な曲線）が与えてあるとする。
>すると、エタール基本群をとることによって自然な完全列ができる：
> 1→ΔX→ΠXp→Gp→1

なるほど
IUTでは、一点抜き楕円曲線X（＝双曲的な曲線）とか、”ｎ一点抜き”などが基本なのか！

>>375-376
省18

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