Remark 90.7.9. In the situation of Lemma 90.7.8 we have maps of complexes

$Lf^*\mathop{N\! L}\nolimits _{S'/S} \to \mathop{N\! L}\nolimits _{X/S'} \to \mathop{N\! L}\nolimits _{X/S}$

These maps are closed to forming a distinguished triangle, see Modules, Lemma 17.31.7. If it were a distinguished triangle we would conclude that the image of $\xi$ in $\mathop{\mathrm{Ext}}\nolimits ^2_{\mathcal{O}_ X}(\mathop{N\! L}\nolimits _{X/S}, \mathcal{G})$ would be the obstruction to the existence of a solution to (90.7.0.1).

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