The Stacks project

Lemma 37.13.10. Let $f : X \to Y$ and $g : Y \to Z$ be morphisms of schemes. There is a canonical six term exact sequence

\[ H^{-1}(f^*\mathop{N\! L}\nolimits _{Y/Z}) \to H^{-1}(\mathop{N\! L}\nolimits _{X/Z}) \to H^{-1}(\mathop{N\! L}\nolimits _{X/Y}) \to f^*\Omega _{Y/Z} \to \Omega _{X/Z} \to \Omega _{X/Y} \to 0 \]

of cohomology sheaves.

Proof. Special case of Modules, Lemma 17.31.7. $\square$

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