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The Stacks project

Lemma 38.6.6. Let R \to S be a finite type ring map. Let M be a finite S-module. Let \mathfrak q be a prime ideal of S. There exists an elementary étale localization R' \to S', \mathfrak q', \mathfrak p' of the ring map R \to S at \mathfrak q such that there exists a complete dévissage of (M \otimes _ S S')/S'/R' at \mathfrak q'.

Proof. This is a reformulation of Proposition 38.5.7 via Remark 38.6.5 \square


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