Completions of quasi-excellent domains
摘要
Let T be a complete local (Noetherian) ring of characteristic zero. We find necessary and sufficient conditions for T to be the completion of a quasi-excellent local domain. In the case that T contains the rationals, we provide necessary and sufficient conditions for T to be the completion of a countable quasi-excellent local domain. We also prove results regarding the possible lengths of maximal saturated chains of prime ideals of these quasi-excellent local domains, and we show that these results lead to interesting examples of noncatenary quasi-excellent local domains.