Journal of Commutative Algebra
- J. Commut. Algebra
- Volume 11, Number 3 (2019), 363-388.
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 $|T| = |T/\mathfrak m|$, 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.
J. Commut. Algebra, Volume 11, Number 3 (2019), 363-388.
First available in Project Euclid: 3 December 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13B35: Completion [See also 13J10]
Secondary: 13J10: Complete rings, completion [See also 13B35]
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