For a locally noetherian scheme $X$, Grothendieck conjectured that if $X$ is quasi-excellent then there is a proper birational map $Y \to X$ s.t. $Y$ is regular.
We now fix an Artin ring $R$ whose residue field $k$ is perfect. Let $X$ be a f.g. scheme over $R$. Under the assumption of resolution of singularities over $k$, the Grothendieck's conjecture is true for $X$.
Question. Under the assumption of resolution of singularities over $k$, is there a proper birational map $Z \to X$ such that $Z$ is smooth over $R$?