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arXiv · 1601.07136

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

Sarah M. Fleming·Lena Ji·S. Loepp·Peter M. McDonald·Nina Pande·David Schwein
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Abstract

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 $\leq$ d $\leq$ dimT-1, 0 $\leq$ t $\leq$ dimT - 1, and d - 1 $\leq$ t. Assume that, for every p in AssT, ht(p) $\leq$ d-1 and that if z is a regular element of T and Q is in Ass(T/zT), then ht(Q) $\leq$ 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.

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Sarah M. Fleming, Lena Ji, S. Loepp, Peter M. McDonald, Nina Pande, David Schwein. 2016-01-26. Controlling the Dimensions of Formal Fibers of a Unique Factorization Domain at the Height One Prime Ideals. https://arxiv.org/abs/1601.07136

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