TITLE: Do arithmetic schemes have non-singular alterations?
QUESTION [7 upvotes]: Let $X$ be an integral normal flat finite type scheme over $\mathbb{Z}$. 


Does there exist a proper surjective generically finite morphism of schemes $Y\to X$ with $Y$ an integral regular finite type scheme over $\mathbb{Z}$?


I could not find such a result in the literature.

REPLY [4 votes]: This is Theorem 8.2 in de Jong's original paper [dJ].
[dJ]  de Jong, A. J., Smoothness, semi-stability and alterations. Publ. Math., Inst. Hautes Étud. Sci. 83, 51-93 (1996). ZBL0916.14005.