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Generic formal fibers and analytically ramified stable rings

Published online by Cambridge University Press:  11 January 2016

Bruce Olberding
Bruce Olberding*
Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001, USA, olberdin@nmsu.edu
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Abstract

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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 d – 1, 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.

Keywords

13E0513B3513B2213F40
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 211 , September 2013 , pp. 109 - 135
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

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