Abstract
Let be a complete local (Noetherian) domain such that . In addition, suppose contains the rationals, , and the set of all principal height-1 prime ideals of has the same cardinality as . We construct a universally catenary local unique factorization domain such that the completion of is and such that there exist uncountably many height-1 prime ideals of such that is a field. Furthermore, in the case where is a normal domain, we can make “close” to excellent in the following sense: the formal fiber at every prime ideal of of height not equal to 1 is geometrically regular, and uncountably many height-1 prime ideals of have geometrically regular formal fibers.
Citation
Sarah M. Fleming. Susan Loepp. "Almost excellent unique factorization domains." Involve 13 (1) 165 - 180, 2020. https://doi.org/10.2140/involve.2020.13.165
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