Nagoya Mathematical Journal

Generic formal fibers and analytically ramified stable rings

Bruce Olberding

Full-text: Open access

Abstract

Let A be a local Noetherian domain of Krull dimension d. Heinzer, Rotthaus, and Sally have shown that if the generic formal fiber of A has dimension d1, then A is birationally dominated by a 1-dimensional analytically ramified local Noetherian ring having residue field finite over the residue field of A. We explore further this correspondence between prime ideals in the generic formal fiber and 1-dimensional analytically ramified local rings. Our main focus is on the case where the analytically ramified local rings are stable, and we show that in this case the embedding dimension of the stable ring reflects the embedding dimension of a prime ideal maximal in the generic formal fiber, thus providing a measure of how far the generic formal fiber deviates from regularity. A number of characterizations of analytically ramified local stable domains are also given.

Article information

Source
Nagoya Math. J., Volume 211 (2013), 109-135.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1367242338

Digital Object Identifier
doi:10.1215/00277630-2148583

Mathematical Reviews number (MathSciNet)
MR3079281

Zentralblatt MATH identifier
1278.13020

Subjects
Primary: 13E05: Noetherian rings and modules 13B35: Completion [See also 13J10] 13B22: Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)
Secondary: 13F40: Excellent rings

Citation

Olberding, Bruce. Generic formal fibers and analytically ramified stable rings. Nagoya Math. J. 211 (2013), 109--135. doi:10.1215/00277630-2148583. https://projecteuclid.org/euclid.nmj/1367242338


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