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Weighted sums of squares in local rings and their completions, II

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2009

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http://nbn-resolving.de/urn:nbn:de:bsz:352-127735
DOI (zitierfähiger Link)
https://doi.org/10.1007/s00209-009-0552-5
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Mathematische Zeitschrift. 2009, 266(1), pp. 21-42. ISSN 0025-5874. Available under: doi: 10.1007/s00209-009-0552-5

Zusammenfassung

Let A be an excellent regular local ring of dimension two, let T be a finitely generated preordering in A, and let T^ be the preordering generated by T in the completion A^ of A. We study the question when the property of being saturated descends from T^ to T, and establish conditions of geometric nature which allow to decide this question. As an application we classify all principal preorderings in A of degree ≤ 3 which are saturated, in the case where A has a real closed residue field. These results have direct implications for nonnegativity certificates for real polynomials on two-dimensional semi-algebraic sets.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Local rings, Completion, Preorderings, Curve singularities, Spaces of orderings, Positive polynomials, Sums of squares, Real algebraic geometry

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ISO 690SCHEIDERER, Claus, 2009. Weighted sums of squares in local rings and their completions, II. In: Mathematische Zeitschrift. 2009, 266(1), pp. 21-42. ISSN 0025-5874. Available under: doi: 10.1007/s00209-009-0552-5
BibTex
@article{Scheiderer2009Weigh-12773,
  year={2009},
  doi={10.1007/s00209-009-0552-5},
  title={Weighted sums of squares in local rings and their completions, II},
  number={1},
  volume={266},
  issn={0025-5874},
  journal={Mathematische Zeitschrift},
  pages={21--42},
  author={Scheiderer, Claus}
}
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