Lemma 10.154.1 (0BSH)—The Stacks project

Processing math: 100%

Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.154: Filtered colimits of étale ring maps
Lemma 10.154.1 (cite)

next lemma

numberstags

history
statistics
2 tags refer to this tag

Lemma 10.154.1. Let $R \to A$ and $R \to R'$ be ring maps. If $A$ is a filtered colimit of étale ring maps, then so is $R' \to R' \otimes _ R A$ .

Proof. This is true because colimits commute with tensor products and étale ring maps are preserved under base change (Lemma 10.143.3). $\square$

Comments (0)

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment