Lemma 15.28.6 (0663)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 15: More on Algebra
Section 15.28: The Koszul complex
Lemma 15.28.6 (cite)

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Lemma 15.28.6. Let $R$ be a ring. Let $f_1, \ldots , f_ r \in R$ be a sequence. Multiplication by $f_ i$ on $K_\bullet (f_\bullet )$ is homotopic to zero, and in particular the cohomology modules $H_ i(K_\bullet (f_\bullet ))$ are annihilated by the ideal $(f_1, \ldots , f_ r)$ .

Proof. Special case of Lemma 15.28.5. $\square$

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