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

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2009

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http://nbn-resolving.de/urn:nbn:de:bsz:352-127724
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https://doi.org/10.1007/s00209-009-0551-6
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Mathematische Zeitschrift. 2009, 266(1), pp. 1-19. ISSN 0025-5874. Available under: doi: 10.1007/s00209-009-0551-6

Zusammenfassung

Let A be an excellent local ring of real dimension ≤2, let T be a finitely generated preordering in A, and let T^ be the preordering generated by T in the completion A^. Under a weak condition on the residue field k = A/m we show that T saturated implies T^ saturated, and that a weak version of the converse holds as well. We also prove a transfer result between different real closed fields in the casewhere A is henselian and k is real closed. These results have direct implications for nonnegativity certificates for real polynomials which are nonnegative on suitable two-dimensional semi-algebraic sets.

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510 Mathematik

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ISO 690SCHEIDERER, Claus, 2009. Weighted sums of squares in local rings and their completions, I. In: Mathematische Zeitschrift. 2009, 266(1), pp. 1-19. ISSN 0025-5874. Available under: doi: 10.1007/s00209-009-0551-6
BibTex
@article{Scheiderer2009Weigh-12772,
  year={2009},
  doi={10.1007/s00209-009-0551-6},
  title={Weighted sums of squares in local rings and their completions, I},
  number={1},
  volume={266},
  issn={0025-5874},
  journal={Mathematische Zeitschrift},
  pages={1--19},
  author={Scheiderer, Claus}
}
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