## Journal of Commutative Algebra

### Completely controlling the dimensions of formal fiber rings at prime ideals of small height

#### 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.

#### Article information

Source
J. Commut. Algebra, Volume 11, Number 3 (2019), 363-388.

Dates
First available in Project Euclid: 3 December 2019

https://projecteuclid.org/euclid.jca/1575363817

Digital Object Identifier
doi:10.1216/JCA-2019-11-3-363

Mathematical Reviews number (MathSciNet)
MR4038055

Zentralblatt MATH identifier
07140752

Subjects

#### Citation

Fleming, Sarah M.; Ji, Lena; Loepp, Susan; McDonald, Peter M.; Pande, Nina; Schwein, David. Completely controlling the dimensions of formal fiber rings at prime ideals of small height. J. Commut. Algebra 11 (2019), no. 3, 363--388. doi:10.1216/JCA-2019-11-3-363. https://projecteuclid.org/euclid.jca/1575363817

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