Lemma 93.8.6 (0ET4)—The Stacks project

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Lemma 93.8.6. In Example 93.8.1 assume $P$ is a finite type $k$ -algebra such that $\mathop{\mathrm{Spec}}(P) \to \mathop{\mathrm{Spec}}(k)$ is smooth except at a finite number of points. Assume $\Lambda$ is a complete local ring with residue field $k$ (the classical case). Then the functor

$F : \mathcal{C}_\Lambda \longrightarrow \textit{Sets},\quad A \longmapsto \mathop{\mathrm{Ob}}\nolimits (\mathcal{D}\! \mathit{ef}_ P(A))/\cong$

of isomorphism classes of objects has a hull.

Proof. This follows immediately from Lemmas 93.8.2 and 93.8.5 and Formal Deformation Theory, Lemma 90.16.6 and Remark 90.15.7. $\square$

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