On the completeness of factor rings

Abstract:

Let $T$ be a complete local domain containing the integers with maximal ideal $M$ such that $|T/M|$ is at least the cardinality of the real numbers. Let $p$ be a nonmaximal prime ideal of $T$ such that $T_{p}$ is a regular local ring. We construct an excellent local ring $A$ such that the completion of $A$ is $T$, the generic formal fiber of $A$ is local with maximal ideal $p$ and if $I$ is a nonzero ideal of $A$, then $A/I$ is complete.