Completely Controlling the Dimensions of Formal Fiber Rings at Prime Ideals of Small Height

Let \(T\) be a complete equicharacteristic local (Noetherian) UFD of dimension \(3\) or greater. Assuming that \(|T| = |T/m|\), where \(m\) is the maximal ideal of \(T\), we construct a local UFD \(A\) whose completion is \(T\) and whose formal fibers at height one prime ideals have prescribed dimen...

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Bibliographic Details
Published in:arXiv.org 2016-04
Main Authors: Fleming, Sarah M, Ji, Lena, Loepp, S, McDonald, Peter M, Pande, Nina, Schwein, David
Format: Article
Language:English
Online Access:Get full text
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Summary:Let \(T\) be a complete equicharacteristic local (Noetherian) UFD of dimension \(3\) or greater. Assuming that \(|T| = |T/m|\), where \(m\) is the maximal ideal of \(T\), we construct a local UFD \(A\) whose completion is \(T\) and whose formal fibers at height one prime ideals have prescribed dimension between zero and the dimension of the generic formal fiber. If, in addition, \(T\) is regular and has characteristic zero, we can construct \(A\) to be excellent.
ISSN:2331-8422