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](https://stacks.math.columbia.edu/tag/07R7), we have the stronger conclusion that $R$ is a filtered colimit of *smooth* $\mathbb{Z}$-algebras.



Is every regular local ring a filtered colimit of essentially finitely generated regular local rings?
It seems it was proved recently by Popescu himself, see [On a question of Swan (with an appendix by Kęstutis Česnavičius)](http://content.algebraicgeometry.nl/2019-6/2019-6-030.pdf).


