The Stacks project

Remark 99.14.14. Lemma 99.14.13 can also be shown using an obstruction theory as in Artin's Axioms, Lemma 98.22.2 (as in the second proof of Lemma 99.5.11). To do this one has to generalize the deformation and obstruction theory developed in Cotangent, Section 92.23 to the case of pairs of algebraic spaces and quasi-coherent modules. Another possibility is to use that the $1$-morphism $\mathcal{P}\! \mathit{olarized}\to \mathcal{S}\! \mathit{paces}'_{fp, flat, proper}$ is algebraic (Lemma 99.14.6) and the fact that we know openness of versality for the target (Lemma 99.13.9 and Remark 99.13.10).