Lemma 15.65.3. Let $R$ be a ring. Let $K^\bullet $ be an object of $D(R)$. Let $a, b \in \mathbf{Z}$. The following are equivalent

$K^\bullet $ has tor-amplitude in $[a, b]$.

$K^\bullet $ is quasi-isomorphic to a complex $E^\bullet $ of flat $R$-modules with $E^ i = 0$ for $i \not\in [a, b]$.

## Comments (2)

Comment #4357 by Manuel Hoff on

Comment #4501 by Johan on

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