it is known from Knutson's work that an algebraic space which is separated and étale over a scheme is a scheme. Let $S$ be a locally noetherian scheme. I am looking for a reference giving an Artin's like criterion as follows: a functor $F:(Sch/S)^{opp} \rightarrow (Set)$ is representable by an algebraic space locally of finite type, étale and quasi-separated over S iff "certain conditions are satisfied". I guess the conditions should contain at least the following: $F$ is an fppf sheaf, $F$ commutes with inductive limits of ring, $F$ commutes with projective adic limits of local artinian rings, and if $A$ is a ring over $S$ and $I\subset A$ is a nilpotent ideal then $F(A)\rightarrow F(A/I)$ is bijective. I would like to add the separation condition $[3^{\prime}](b)$ of theorem 5.3 in Artin's paper "Algebraization of formal moduli: I" to complete the list, but I am not sure if this is enough.


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