Can somebody give me an explicit example of a Noetherian local domain A which does not have resolution of singularities? In particular, I would like an example where the completion A^{*} of A defines an isolated singularity, i.e., where Spec(A^{*}) – {m^{*}} is a regular scheme?

A related question (I think) is this: Does there exist a Noetherian local ring A such that there exists a proper morphism Y —> Spec(A^{*}) whose source Y is an algebraic space which is an isomorphism over the punctured spectrum such that Y is **not** isomorphic to the base change of a proper morphism X —> Spec(A) whose source is an algebraic space? [**Edit 20 October 2014:** This cannot happen; follow link below.]

I wanted to make an example for the second question by taking a Noetherian local ring A which does not have a resolution whose completion A^{*} is a domain and defines an isolated singularity. Then a resolution of singularities Y of A^{*} would presumably not be the base change of an X, because if so then X would presumably be a resolution for A. [**Edit 20 October 2014:** This cannot happen; follow link below.]

Anyway, I searched for examples of this sort on the web but failed to find a relevant example. Can you help? Thanks!

[**Edit 23 July 2014:** The discussion is continued in this blog post.]