Lemma 37.13.16. Consider a cartesian diagram of schemes

If $X \to Y$ is flat, then the canonical map $(g')^*\mathop{N\! L}\nolimits _{X/Y} \to \mathop{N\! L}\nolimits _{X'/Y'}$ is a quasi-isomorphism. If in addition $\mathop{N\! L}\nolimits _{X/Y}$ has tor-amplitude in $[-1, 0]$ then $L(g')^*\mathop{N\! L}\nolimits _{X/Y} \to \mathop{N\! L}\nolimits _{X'/Y'}$ is a quasi-isomorphism too.

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