Controlling the Dimensions of Formal Fibers of a Unique Factorization Domain at the Height One Prime Ideals

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Let T be a complete local (Noetherian) equidimensional ring with maximal ideal m such that the Krull dimension of T is at least two and the depth of T is at least two. Suppose that no integer of T is a zerodivisor and that |T|=|T/m|. Let d and t be integers such that 1 ≤ d ≤ dimT-1, 0 ≤ t ≤ dimT - 1, and d - 1 ≤ t. Assume that, for every p in AssT, ht(p) ≤ d-1 and that if z is a regular element of T and Q is in Ass(T/zT), then ht(Q) ≤ d. We construct a local unique factorization domain A such that the completion of A is T and such that the dimension of the formal fiber ring at every height one prime ideal of A is d - 1 and the dimension of the formal fiber ring of A at (0) is t.