Lemma 42.68.32 (0AY9)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 42: Chow Homology and Chern Classes
Section 42.68: Appendix A: Alternative approach to key lemma
Lemma 42.68.32 (cite)

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Lemma 42.68.32. Let $A$ be a Noetherian local ring and $M$ a finite $A$ -module of dimension $1$ . Let $a \in A$ be a nonzerodivisor on $M$ . Then $d_ M(a, a) = (-1)^{\text{length}_ A(M/aM)}$ .

Proof. Immediate from Lemma 42.68.16. $\square$

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