Lemma 37.62.16. 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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