Lemma 90.19.12 (06JZ)—The Stacks project

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Table of contents
Part 6: Deformation Theory
Chapter 90: Formal Deformation Theory
Section 90.19: Infinitesimal automorphisms
Lemma 90.19.12 (cite)

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Lemma 90.19.12. Let $\mathcal{F}$ be a category cofibered in groupoids over $\mathcal{C}_\Lambda$ satisfying (RS). Let $x' \to x$ be a morphism in $\mathcal{F}$ lying over a surjective ring map. Let $x_0$ be a pushforward of $x$ to $\mathcal{F}(k)$ . If $\text{Inf}_{x_0}(\mathcal{F}) = 0$ then $\text{Inf}(x'/x) = 0$ .

Proof. Follows from Lemmas 90.3.3 and 90.19.11. $\square$

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