Lemma 16.8.2 (07F3)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 16: Smoothing Ring Maps
Section 16.8: Warmup: reduction to a base field
Lemma 16.8.2 (cite)

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Lemma 16.8.2. Let $R_ i \to \Lambda _ i$ , $i = 1, 2$ be as in Situation 16.8.1. If PT holds for $R_ i \to \Lambda _ i$ , $i = 1, 2$ , then PT holds for $R_1 \times R_2 \to \Lambda _1 \times \Lambda _2$ .

Proof. Omitted. Hint: A product of filtered colimits is a filtered colimit. $\square$

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