Lemma 37.54.15. Let $f : X \to Y$ be a local complete intersection homomorphism. Then the naive cotangent complex $\mathop{N\! L}\nolimits _{X/Y}$ is a perfect object of $D(\mathcal{O}_ X)$ of tor-amplitude in $[-1, 0]$.

**Proof.**
Translated into algebra this is More on Algebra, Lemma 15.79.4. To do the translation use Lemmas 37.54.5 and 37.13.2 as well as Derived Categories of Schemes, Lemmas 36.3.5, 36.9.4 and 36.9.7.
$\square$

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