Pointwise surjective presentations of stacks

Abstract

We show that any stack of finite type over a Noetherian scheme has a presentation by a scheme of finite type such that is onto, for every finite or real closed field F. Under some additional conditions on we show the same for all perfect fields. We prove similar results for (some) Henselian rings. We give two applications of the main result. One is to counting isomorphism classes of stacks over the rings the other is about the relation between real algebraic and Nash stacks.