Lemma 37.60.16. Let $f : X \to Y$ be a perfect morphism of locally Noetherian schemes. The following are equivalent

$f$ is a local complete intersection morphism,

$\mathop{N\! L}\nolimits _{X/Y}$ has tor-amplitude in $[-1, 0]$, and

$\mathop{N\! L}\nolimits _{X/Y}$ is perfect with tor-amplitude in $[-1, 0]$.

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