Lemma 10.109.7. Let $R$ be a local Noetherian ring. Let $M$ be a finite $R$-module. Let $d \geq 0$. The equivalent conditions (1) – (4) of Lemma 10.109.4, condition (5) of Lemma 10.109.5, and condition (6) of Lemma 10.109.6 are also equivalent to

there exists a resolution $0 \to F_ d \to F_{d - 1} \to \ldots \to F_0 \to M \to 0$ with $F_ i$ finite free.

## Comments (2)

Comment #2529 by Oleksandr Kravets on

Comment #2565 by Johan on

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