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

@article{Fleming2019CompletelyCT, title={Completely controlling the dimensions of formal fiber rings at prime ideals of small height}, author={Sarah M. Fleming and Lena Ji and Susan Loepp and Peter M. McDonald and Nina Pande and David Schwein}, journal={Journal of Commutative Algebra}, year={2019} }

Let $T$ be a complete equicharacteristic local (Noetherian) UFD of dimension $3$ or greater. Assuming that $|T| = |T/m|$, where $m$ 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.

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SHOWING 1-9 OF 9 REFERENCES

Dimensions of Formal Fibers of Height One Prime Ideals

- Mathematics
- 2009

Let T be a complete local (Noetherian) ring with maximal ideal M, P a nonmaximal ideal of T, and C = {Q 1, Q 2,…} a (nonempty) finite or countable set of nonmaximal prime ideals of T. Let {p 1, p… Expand

Semilocal generic formal fibers

- Mathematics
- 2003

Abstract Let T be a complete local ring and C a finite set of incomparable prime ideals of T . We find necessary and sufficient conditions for T to be the completion of an integral domain whose… Expand

Constructing Local Generic Formal Fibers

- Mathematics
- 1997

Abstract Let ( T , M ) be a complete local (Noetherian) unique factorization domain of dimension at least two such that the cardinality of the residue field T / M is at least the cardinality of the… Expand

Completions of Local Rings with an Isolated Singularity

- Mathematics
- 1994

Abstract It is shown that all equicharacteristic complete local rings can be realized as completions of local rings whose proper localizations are all regular. The only restriction in the mixed… Expand

Characterization of completions of unique factorization domains

- Mathematics
- 1993

It is shown that a complete local ring is the completion of a unique factorization domain if and only if it is a field, a discrete valuation ring, or it has depth at least two and no element of its… Expand

Charters and S . Loepp , Semilocal generic formal fibers

- J . Algebra
- 2004