Lemma 9.22.5 (0BMM)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 9: Fields
Section 9.22: Infinite Galois theory
Lemma 9.22.5 (cite)

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Lemma 9.22.5. Let $L/M/K$ be a tower of fields. Assume $L/K$ and $M/K$ are Galois. Then we obtain a short exact sequence

$1 \to \text{Gal}(L/M) \to \text{Gal}(L/K) \to \text{Gal}(M/K) \to 1$

of profinite topological groups.

Proof. This is a reformulation of Lemma 9.22.2. $\square$

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