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September 2013 Generic formal fibers and analytically ramified stable rings
Bruce Olberding
Nagoya Math. J. 211: 109-135 (September 2013). DOI: 10.1215/00277630-2148583


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.


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Bruce Olberding. "Generic formal fibers and analytically ramified stable rings." Nagoya Math. J. 211 109 - 135, September 2013.


Published: September 2013
First available in Project Euclid: 29 April 2013

zbMATH: 1278.13020
MathSciNet: MR3079281
Digital Object Identifier: 10.1215/00277630-2148583

Primary: 13B22 , 13B35 , 13E05
Secondary: 13F40

Rights: Copyright © 2013 Editorial Board, Nagoya Mathematical Journal


Vol.211 • September 2013
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