Every Finite Poset is Isomorphic to a Saturated Subset of the Spectrum of a Noetherian UFD

Abstract

We show that every finite poset is isomorphic to a saturated subset of the spectrum of a Noetherian unique factorization domain. In addition, we show that every finite poset is isomorphic to a saturated subset of the spectrum of a quasi-excellent domain.

arXiv commentArguments in Sections 5 and 6 of the original version have been simplified, a mathematical error in Section 4 of the original version has been fixed