Proposition 10.83.3 (058S)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.83: Descent for finite projective modules
Proposition 10.83.3 (cite)

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Proposition 10.83.3. Let $R \to S$ be a faithfully flat ring map. Let $M$ be an $R$ -module. If the $S$ -module $M \otimes _ R S$ is finite projective, then $M$ is finite projective.

Proof. Follows from Lemmas 10.83.1 and 10.83.2. $\square$

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