Artin/Popescu approximation for (some) big rings - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T13:37:38Z http://mathoverflow.net/feeds/question/106928 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106928/artin-popescu-approximation-for-some-big-rings Artin/Popescu approximation for (some) big rings anon 2012-09-11T16:23:10Z 2012-09-11T16:23:10Z <p>Fix a prime number $p$. Let $A = \overline{\mathbf{Z}_p}$ be the integral closure of the $p$-adic integers $\mathbf{Z}_p$ in some fixed algebraic closure of its fraction field, and let $B$ be the $p$-adic completion of $A$. Is the map $A \to B$ an inductive limit of smooth morphisms? If $A$ was excellent, this would follow from Artin/Popescu approximation theorems, but $A$ is not even noetherian. Of course, one can ask similar questions much more generally, but this is the case I am interested in.</p>