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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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

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

First available in Project Euclid: 3 December 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13B35: Completion [See also 13J10]
Secondary: 13J10: Complete rings, completion [See also 13B35]

Completions of local rings formal fibers


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.

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