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On local uniformization of orderings

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Andradas Heranz, Carlos and Ruiz Sancho, Jesús María (1994) On local uniformization of orderings. In Recent advances in real algebraic geometry and quadratic forms. Contemporary mathematics (155). American Mathematical Society, Providence, R.I, pp. 19-46. ISBN 0-8218-5154-3

Official URL: http://www.ams.org/books/conm/155/




Abstract

The main application of the results of this paper is to prove the existence of real valuation rings of the quotient field K of an excellent domain A having prescribed centers, ranks, rational ranks and residue dimensions. The major part of the paper develops the machinery necessary for this task. Let α be a point in the real spectrum of the ring A. Much of the paper is devoted to showing that α can be uniformized by means of quadratic transforms. Assume now that A is local. Write Gα for the topological space of all generations of α in the quotient field K, write Uα for the subset of elements βGα which uniformize α, and write Bα for the set of βGα which blow up α. The two main theorems state that the interior of Uα is dense in Gα and that the set Bα is dense in Gα.


Item Type:Book Section
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Proceedings of the RAGSQUAD year, Berkeley, 1990-1991.
Papers resulting from a course held at the University of California at Berkeley, 1990-91 and the AMS Special Session on Real Algebraic Geometry and Quadratic Forms held in San Francisco, Jan. 1991, both comprising the special year dubbed RAGSQUAD

Uncontrolled Keywords:Uniformization of orderings; excellent rings; existence of real valuation rings; solving singularities
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:21329
Deposited On:14 May 2013 15:49
Last Modified:12 Dec 2018 15:13

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