Remark 48.12.9. Lemma 48.12.8 means our relative dualizing complex is *rigid* in a sense analogous to the notion introduced in [vdB-rigid]. Namely, since the functor on the right of (48.12.8.2) is “quadratic” in $\omega _{X/Y}^\bullet $ and the functor on the left of (48.12.8.2) is “linear” this “pins down” the complex $\omega _{X/Y}^\bullet $ to some extent. There is an approach to duality theory using “rigid” (relative) dualizing complexes, see for example [Neeman-rigid], [Yekutieli-rigid], and [Yekutieli-Zhang]. We will return to this in Section 48.28.

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