## Journal of Commutative Algebra

### Controlling the generic formal fiber of local domains and their polynomial rings

#### Abstract

Let $T$ be a complete local ring with maximal ideal $M$, $C$ a countable set of incomparable prime ideals of $T$, and $B_1$ and $B_2$ sets of prime ideals of $T[[x_1,\ldots,x_n]]$ with cardinality less than that of $T$. We present necessary and sufficient conditions for the existence of a local domain $A$ with completion $T$, such that the generic formal fiber of $A$ has maximal elements equal to the ideals in $C$ and the generic formal fiber of $A[x_1,\ldots,x_n]_{(M\cap A,x_1,\ldots,x_n)}$ contains every element of $B_1$ but no element of $B_2$. If $T$ has characteristic $0$, we present necessary and sufficient conditions for the existence of an excellent local domain $A$ with the above properties.

#### Article information

Source
J. Commut. Algebra, Volume 7, Number 2 (2015), 241-264.

Dates
First available in Project Euclid: 14 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.jca/1436909534

Digital Object Identifier
doi:10.1216/JCA-2015-7-2-241

Mathematical Reviews number (MathSciNet)
MR3370486

Zentralblatt MATH identifier
1354.13032

#### Citation

Jiang, Peihong; Kirkpatrick, Anna; Loepp, S.; Mack-Crane, Sander; Tripp, S. Controlling the generic formal fiber of local domains and their polynomial rings. J. Commut. Algebra 7 (2015), no. 2, 241--264. doi:10.1216/JCA-2015-7-2-241. https://projecteuclid.org/euclid.jca/1436909534