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2019 Completely controlling the dimensions of formal fiber rings at prime ideals of small height
Sarah M. Fleming, Lena Ji, Susan Loepp, Peter M. McDonald, Nina Pande, David Schwein
J. Commut. Algebra 11(3): 363-388 (2019). DOI: 10.1216/JCA-2019-11-3-363

Abstract

Let $T$ be a complete equicharacteristic local (Noetherian) UFD of dimension $3$ or greater. Assuming that $|T| = |T/\mathfrak m|$, where $\mathfrak m$ 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.

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Sarah M. Fleming. Lena Ji. Susan Loepp. Peter M. McDonald. Nina Pande. David Schwein. "Completely controlling the dimensions of formal fiber rings at prime ideals of small height." J. Commut. Algebra 11 (3) 363 - 388, 2019. https://doi.org/10.1216/JCA-2019-11-3-363

Information

Published: 2019
First available in Project Euclid: 3 December 2019

zbMATH: 07140752
MathSciNet: MR4038055
Digital Object Identifier: 10.1216/JCA-2019-11-3-363

Subjects:
Primary: 13B35
Secondary: 13J10

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.11 • No. 3 • 2019
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