We prove a generalization of the Jacobian criterion of Fargues-Scholze for spaces of sections of a scheme smooth quasi-projective over the algebraic Fargues-Fontaine curve [8, Section IV.4]. Namely, we show how to use their criterion to deduce an analogue for spaces of sections of a smooth Artin stack over the algebraic curve obtained by taking the stack quotient of such a relatively smooth quasi-projective scheme by the action of a linear algebraic group. As an application, we show various moduli stacks appearing in the Fargues-Scholze geometric Langlands program are cohomologically smooth Artin v-stacks and compute their \(\ell \) -dimensions.
