Constructing almost excellent unique factorization domains

摘要

Let (T, M) be a complete local normal integral domain containing the rationals such that T/M >= c where c is the cardinality of the real numbers. Let p be a non-maximal prime ideal of T such that T-p is a regular local ring. We construct a local Unique Factorization Domain (UFD) A smelt that the M-adic completion of A is T, p is maximal in the generic formal fiber and all fibers of A are geometrically regular except for those over some height one prime ideals.