Lemma 48.15.6. Let $Y$ be a quasi-compact and quasi-separated scheme. Let $i : X \to Y$ be a Koszul-regular closed immersion. Let $a$ be the right adjoint of $Ri_* : D_\mathit{QCoh}(\mathcal{O}_ X) \to D_\mathit{QCoh}(\mathcal{O}_ Y)$ of Lemma 48.3.1. Then there is an isomorphism

where $\mathcal{N} = \mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ X}(\mathcal{C}_{X/Y}, \mathcal{O}_ X)$ is the normal sheaf of $i$ (Morphisms, Section 29.31) and $r$ is its rank viewed as a locally constant function on $X$.

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