Real Algebraic and Analytic Geometry
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22. C. Andradas, A. Díaz-Cano:
Closed stability index of excellent henselian local rings.

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Submission: 2002, October 30.

Abstract:
We show that the closed stability index of an excellent henselian local ring of dimension $d > 2$ with real closed residue field is $\ol s(A)=\frac{1}{2}d(d+1)$. When $d=2$ it is shown that the value of $\ol s(A)$ can be be either 2 or 3 and give characterizations of each of these values in terms of the relation of $A$ with its normalization and in terms of the real spectrum of $A$.

Mathematics Subject Classification (2000): 14P15, 32B10, 32B20.

Keywords and Phrases: stability index, constructible sets, real spectrum, excellent rings.

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