Journal of Commutative Algebra

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, and David Schwein

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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

Permanent link to this document
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
Primary: 13B35: Completion [See also 13J10]
Secondary: 13J10: Complete rings, completion [See also 13B35]

Keywords
Completions of local rings formal fibers

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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References

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