# Is every regular local ring a filtered colimit of essentially finitely generated regular local rings?

Is every regular local ring $$R$$ a filtered colimit of regular local rings which are essentially of finite type over $$\mathbb{Z}$$ (i.e. localizations of finitely generated rings)?

For comparison, Popescu's theorem says that under the stronger assumption that $$\mathrm{Spec}\,R\to\mathrm{Spec}\,\mathbb{Z}$$ is a regular morphism, we have the stronger conclusion that $$R$$ is a filtered colimit of smooth $$\mathbb{Z}$$-algebras.