Lemma 15.116.1 (0GLR)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 15: More on Algebra
Section 15.116: Eliminating ramification, II
Lemma 15.116.1 (cite)

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Lemma 15.116.1. Let $A \to B$ be an extension of discrete valuation rings with fraction fields $K \subset L$ . If $K_1/K$ is a solution for $A \subset B$ , then for any finite extension $K_2/K_1$ the extension $K_2/K$ is a solution for $A \subset B$ .

Proof. This follows from Lemma 15.114.3. Details omitted. $\square$

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